Algebra 1
1st Edition
ISBN: 9780078884801
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Question
Chapter 5.1, Problem 55HP
To determine
Write the process of solving and linear graphing.
Expert Solution & Answer
Answer to Problem 55HP
Explanation of Solution
Concept Used:
Rules for solving inequality equations:
These things do not affect the direction of the inequality:
- Add (or subtract) a number from both sides
- Multiply (or divide) both sides by a positive number
- Simplify a side
But these things do change the direction of the inequality ("
- Multiply (or divide) both sides by a negative number
- Swapping left and right hand sides
For Inequality equation: If
Example:
| Steps | Explanation |
| Original equation Subtract 14 from both sides. Divide each side by 2 Solution:
| |
| Original Equation Subtract 7x from both sides.
|
Here is a summary of how to graph inequalities:
1) Draw a number line.2) Put either an open circle or a closed dot above the number given.
For ≤ and ≥ , use a closed dot to indicate the number itself is part of the solution.
For < and >, use an open circle to indicate the number itself is not part of the solution.
3) Choose which way the arrow should go. Either think about which numbers would be part of the solution. Or, as long as the variable is listed first, you can just look at the symbol
For ≤ and <, the arrow points down to the left.
For ≥ and >, the arrow points up to the right.
|
Plotting inequalities: To plot an inequality: Such as x>3, on a number line, first draw a circle over the number (e.g., 3). Then if the sign includes equal to (= or =), fill in the circle (solid circle). If the sign does not include equal to (> or <), leave the circle (hollow circle) unfilled in. For x < 3 or x >3, there is a hollow circle. For |  |
Thus, solving linear inequalities is similar to solving linear equations. You must isolate the variable on one side of the inequality.
To graph, if the problem is a less than or a greater than inequality, an open circle is used. Otherwise a dot is used.
If the variable is on the left hand side of the inequality, and the inequality sign is less than (or less than or equal to), the graph extends to the left; otherwise it extends to the right.
Chapter 5 Solutions
Algebra 1
Ch. 5.1 - Prob. 1ACYPCh. 5.1 - Prob. 1BCYPCh. 5.1 - Prob. 2CYPCh. 5.1 - Prob. 3ACYPCh. 5.1 - Prob. 3BCYPCh. 5.1 - Prob. 4CYPCh. 5.1 - Prob. 1CYUCh. 5.1 - Prob. 2CYUCh. 5.1 - Prob. 3CYUCh. 5.1 - Prob. 4CYU
Ch. 5.1 - Prob. 5CYUCh. 5.1 - Prob. 6CYUCh. 5.1 - Prob. 7CYUCh. 5.1 - Prob. 8CYUCh. 5.1 - Prob. 9CYUCh. 5.1 - Prob. 10CYUCh. 5.1 - Prob. 11CYUCh. 5.1 - Prob. 12PPSCh. 5.1 - Prob. 13PPSCh. 5.1 - Prob. 14PPSCh. 5.1 - Prob. 15PPSCh. 5.1 - Prob. 16PPSCh. 5.1 - Prob. 17PPSCh. 5.1 - Prob. 18PPSCh. 5.1 - Prob. 19PPSCh. 5.1 - Prob. 20PPSCh. 5.1 - Prob. 21PPSCh. 5.1 - Prob. 22PPSCh. 5.1 - Prob. 23PPSCh. 5.1 - Prob. 24PPSCh. 5.1 - Prob. 25PPSCh. 5.1 - Prob. 26PPSCh. 5.1 - Prob. 27PPSCh. 5.1 - Prob. 28PPSCh. 5.1 - Prob. 29PPSCh. 5.1 - Prob. 30PPSCh. 5.1 - Prob. 31PPSCh. 5.1 - Prob. 32PPSCh. 5.1 - Prob. 33PPSCh. 5.1 - Prob. 34PPSCh. 5.1 - Prob. 35PPSCh. 5.1 - Prob. 36PPSCh. 5.1 - Prob. 37PPSCh. 5.1 - Prob. 38PPSCh. 5.1 - Prob. 39PPSCh. 5.1 - Prob. 40PPSCh. 5.1 - Prob. 41PPSCh. 5.1 - Prob. 42PPSCh. 5.1 - Prob. 43PPSCh. 5.1 - Prob. 44PPSCh. 5.1 - Prob. 45PPSCh. 5.1 - Prob. 46PPSCh. 5.1 - Prob. 47PPSCh. 5.1 - Prob. 48PPSCh. 5.1 - Prob. 49PPSCh. 5.1 - Prob. 50PPSCh. 5.1 - Prob. 51PPSCh. 5.1 - Prob. 52HPCh. 5.1 - 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Prob. 1BCYPCh. 5.4 - Prob. 2BCYPCh. 5.4 - Prob. 3ACYPCh. 5.4 - Prob. 3BCYPCh. 5.4 - Prob. 1CYUCh. 5.4 - Prob. 2CYUCh. 5.4 - Prob. 3CYUCh. 5.4 - Prob. 4CYUCh. 5.4 - Prob. 5CYUCh. 5.4 - Prob. 6PPSCh. 5.4 - Prob. 7PPSCh. 5.4 - Prob. 8PPSCh. 5.4 - Prob. 9PPSCh. 5.4 - Prob. 10PPSCh. 5.4 - Prob. 11PPSCh. 5.4 - Prob. 12PPSCh. 5.4 - Prob. 13PPSCh. 5.4 - Prob. 14PPSCh. 5.4 - Prob. 15PPSCh. 5.4 - Prob. 16PPSCh. 5.4 - Prob. 17PPSCh. 5.4 - Prob. 18PPSCh. 5.4 - Prob. 19PPSCh. 5.4 - Prob. 20PPSCh. 5.4 - Prob. 21PPSCh. 5.4 - Prob. 22PPSCh. 5.4 - Prob. 23PPSCh. 5.4 - Prob. 24PPSCh. 5.4 - Prob. 25PPSCh. 5.4 - Prob. 26PPSCh. 5.4 - Prob. 27PPSCh. 5.4 - Prob. 28PPSCh. 5.4 - Prob. 29PPSCh. 5.4 - Prob. 30PPSCh. 5.4 - Prob. 31PPSCh. 5.4 - Prob. 32PPSCh. 5.4 - Prob. 33PPSCh. 5.4 - Prob. 34PPSCh. 5.4 - Prob. 35PPSCh. 5.4 - Prob. 36PPSCh. 5.4 - Prob. 37PPSCh. 5.4 - Prob. 38PPSCh. 5.4 - Prob. 39HPCh. 5.4 - Prob. 40HPCh. 5.4 - Prob. 41HPCh. 5.4 - Prob. 42HPCh. 5.4 - Prob. 43HPCh. 5.4 - Prob. 44STPCh. 5.4 - Prob. 45STPCh. 5.4 - Prob. 46STPCh. 5.4 - Prob. 47STPCh. 5.4 - Prob. 48SRCh. 5.4 - Prob. 49SRCh. 5.4 - Prob. 50SRCh. 5.4 - Prob. 51SRCh. 5.4 - Prob. 52SRCh. 5.4 - Prob. 53SRCh. 5.4 - Prob. 54SRCh. 5.4 - Prob. 55SRCh. 5.4 - Prob. 56SRCh. 5.4 - Prob. 57SRCh. 5.4 - Prob. 58SRCh. 5.4 - Prob. 59SRCh. 5.4 - Prob. 60SRCh. 5.4 - Prob. 61SRCh. 5.4 - Prob. 62SRCh. 5.4 - Prob. 63SRCh. 5.4 - Prob. 64SCh. 5.4 - Prob. 65SCh. 5.4 - Prob. 66SCh. 5.4 - Prob. 67SCh. 5.4 - Prob. 68SCh. 5.4 - Prob. 69SCh. 5.4 - Prob. 70SCh. 5.4 - Prob. 71SCh. 5.4 - Prob. 72SCh. 5.5 - Prob. 1BCYPCh. 5.5 - Prob. 2CYPCh. 5.5 - Prob. 3ACYPCh. 5.5 - Prob. 3BCYPCh. 5.5 - Prob. 20PPSCh. 5.5 - Prob. 24PPSCh. 5.5 - Prob. 25PPSCh. 5.5 - Prob. 26PPSCh. 5.5 - Prob. 27PPSCh. 5.5 - Prob. 28PPSCh. 5.5 - Prob. 29PPSCh. 5.5 - Prob. 32PPSCh. 5.5 - Prob. 33PPSCh. 5.5 - Prob. 34PPSCh. 5.5 - Prob. 35PPSCh. 5.5 - Prob. 36PPSCh. 5.5 - Prob. 37PPSCh. 5.5 - Prob. 38PPSCh. 5.5 - Prob. 39PPSCh. 5.5 - Prob. 40PPSCh. 5.5 - Prob. 41PPSCh. 5.5 - Prob. 43HPCh. 5.5 - Prob. 44HPCh. 5.5 - Prob. 45HPCh. 5.5 - Prob. 1ACYPCh. 5.5 - Prob. 1CYUCh. 5.5 - Prob. 2CYUCh. 5.5 - Prob. 3CYUCh. 5.5 - Prob. 4CYUCh. 5.5 - Prob. 5CYUCh. 5.5 - Prob. 6CYUCh. 5.5 - Prob. 7CYUCh. 5.5 - Prob. 8PPSCh. 5.5 - Prob. 9PPSCh. 5.5 - Prob. 10PPSCh. 5.5 - Prob. 11PPSCh. 5.5 - Prob. 12PPSCh. 5.5 - Prob. 13PPSCh. 5.5 - Prob. 14PPSCh. 5.5 - Prob. 15PPSCh. 5.5 - Prob. 16PPSCh. 5.5 - Prob. 17PPSCh. 5.5 - Prob. 18PPSCh. 5.5 - Prob. 19PPSCh. 5.5 - Prob. 21PPSCh. 5.5 - Prob. 22PPSCh. 5.5 - Prob. 23PPSCh. 5.5 - Prob. 30PPSCh. 5.5 - Prob. 31PPSCh. 5.5 - Prob. 42PPSCh. 5.5 - Prob. 46HPCh. 5.5 - Prob. 47HPCh. 5.5 - Prob. 48STPCh. 5.5 - Prob. 49STPCh. 5.5 - Prob. 50STPCh. 5.5 - Prob. 51STPCh. 5.5 - Prob. 52SRCh. 5.5 - Prob. 53SRCh. 5.5 - Prob. 54SRCh. 5.5 - Prob. 55SRCh. 5.5 - Prob. 56SRCh. 5.5 - Prob. 57SRCh. 5.5 - Prob. 58SRCh. 5.5 - Prob. 59SRCh. 5.5 - Prob. 60SRCh. 5.5 - Prob. 61SCh. 5.5 - Prob. 62SCh. 5.5 - Prob. 63SCh. 5.5 - Prob. 64SCh. 5.5 - Prob. 65SCh. 5.5 - Prob. 66SCh. 5.5 - Prob. 67SCh. 5.5 - Prob. 68SCh. 5.6 - Prob. 13PPSCh. 5.6 - Prob. 14PPSCh. 5.6 - Prob. 15PPSCh. 5.6 - Prob. 16PPSCh. 5.6 - Prob. 17PPSCh. 5.6 - Prob. 20PPSCh. 5.6 - Prob. 21PPSCh. 5.6 - Prob. 22PPSCh. 5.6 - Prob. 25PPSCh. 5.6 - Prob. 1ACYPCh. 5.6 - Prob. 1BCYPCh. 5.6 - Prob. 2ACYPCh. 5.6 - Prob. 2BCYPCh. 5.6 - Prob. 3ACYPCh. 5.6 - Prob. 3BCYPCh. 5.6 - Prob. 4CYPCh. 5.6 - Prob. 1CYUCh. 5.6 - Prob. 2CYUCh. 5.6 - Prob. 3CYUCh. 5.6 - Prob. 4CYUCh. 5.6 - Prob. 5CYUCh. 5.6 - Prob. 6CYUCh. 5.6 - Prob. 7CYUCh. 5.6 - Prob. 8CYUCh. 5.6 - Prob. 9CYUCh. 5.6 - Prob. 10CYUCh. 5.6 - Prob. 11CYUCh. 5.6 - Prob. 12PPSCh. 5.6 - Prob. 18PPSCh. 5.6 - Prob. 19PPSCh. 5.6 - Prob. 23PPSCh. 5.6 - Prob. 24PPSCh. 5.6 - Prob. 26PPSCh. 5.6 - Prob. 27PPSCh. 5.6 - Prob. 28PPSCh. 5.6 - Prob. 29PPSCh. 5.6 - Prob. 30PPSCh. 5.6 - Prob. 31PPSCh. 5.6 - Prob. 32PPSCh. 5.6 - Prob. 33PPSCh. 5.6 - Prob. 34PPSCh. 5.6 - Prob. 35PPSCh. 5.6 - Prob. 36PPSCh. 5.6 - Prob. 37PPSCh. 5.6 - Prob. 38PPSCh. 5.6 - Prob. 39PPSCh. 5.6 - Prob. 40PPSCh. 5.6 - Prob. 41PPSCh. 5.6 - Prob. 42PPSCh. 5.6 - Prob. 43PPSCh. 5.6 - Prob. 44PPSCh. 5.6 - Prob. 45PPSCh. 5.6 - Prob. 46HPCh. 5.6 - Prob. 47HPCh. 5.6 - Prob. 48HPCh. 5.6 - Prob. 49HPCh. 5.6 - Prob. 50HPCh. 5.6 - Prob. 51STPCh. 5.6 - Prob. 52STPCh. 5.6 - Prob. 53STPCh. 5.6 - Prob. 54STPCh. 5.6 - Prob. 55SRCh. 5.6 - Prob. 56SRCh. 5.6 - Prob. 57SRCh. 5.6 - Prob. 58SRCh. 5.6 - Prob. 59SRCh. 5.6 - Prob. 60SRCh. 5.6 - Prob. 61SRCh. 5.6 - Prob. 62SRCh. 5.6 - Prob. 63SRCh. 5.6 - Prob. 64SRCh. 5.6 - Prob. 65SCh. 5 - Prob. 1SGRCh. 5 - Prob. 2SGRCh. 5 - Prob. 3SGRCh. 5 - Prob. 4SGRCh. 5 - Prob. 5SGRCh. 5 - Prob. 6SGRCh. 5 - Prob. 7SGRCh. 5 - Prob. 9SGRCh. 5 - Prob. 10SGRCh. 5 - Prob. 11SGRCh. 5 - Prob. 12SGRCh. 5 - Prob. 13SGRCh. 5 - Prob. 14SGRCh. 5 - Prob. 15SGRCh. 5 - Prob. 16SGRCh. 5 - Prob. 17SGRCh. 5 - Prob. 18SGRCh. 5 - Prob. 20SGRCh. 5 - Prob. 21SGRCh. 5 - Prob. 22SGRCh. 5 - Prob. 23SGRCh. 5 - Prob. 24SGRCh. 5 - Prob. 25SGRCh. 5 - Prob. 26SGRCh. 5 - Prob. 30SGRCh. 5 - Prob. 41SGRCh. 5 - Prob. 44SGRCh. 5 - Prob. 46SGRCh. 5 - Prob. 47SGRCh. 5 - Prob. 48SGRCh. 5 - Prob. 49SGRCh. 5 - Prob. 50SGRCh. 5 - Prob. 51SGRCh. 5 - Prob. 52SGRCh. 5 - Prob. 53SGRCh. 5 - Prob. 15PTCh. 5 - Prob. 16PTCh. 5 - Prob. 19PTCh. 5 - Prob. 20PTCh. 5 - Prob. 21PTCh. 5 - Prob. 22PTCh. 5 - Prob. 23PTCh. 5 - Prob. 24PTCh. 5 - Prob. 1QCCh. 5 - Prob. 2QCCh. 5 - Prob. 3QCCh. 5 - Prob. 4QCCh. 5 - Prob. 5QCCh. 5 - Prob. 6QCCh. 5 - Prob. 7QCCh. 5 - Prob. 8QCCh. 5 - Prob. 9QCCh. 5 - Prob. 10QCCh. 5 - Prob. 11QCCh. 5 - Prob. 12QCCh. 5 - Prob. 13QCCh. 5 - Prob. 14QCCh. 5 - Prob. 15QCCh. 5 - Prob. 1MCQCh. 5 - Prob. 2MCQCh. 5 - Prob. 3MCQCh. 5 - Prob. 4MCQCh. 5 - Prob. 5MCQCh. 5 - Prob. 6MCQCh. 5 - Prob. 7MCQCh. 5 - Prob. 8MCQCh. 5 - Prob. 9MCQCh. 5 - Prob. 10MCQCh. 5 - Prob. 11MCQCh. 5 - Prob. 12MCQCh. 5 - Prob. 13MCQCh. 5 - Prob. 14MCQCh. 5 - Prob. 15MCQCh. 5 - Prob. 16MCQCh. 5 - Prob. 17MCQCh. 5 - Prob. 18MCQCh. 5 - Prob. 19MCQCh. 5 - Prob. 20MCQCh. 5 - Prob. 21MCQCh. 5 - Prob. 22MCQCh. 5 - Prob. 23MCQCh. 5 - Prob. 24MCQCh. 5 - Prob. 25MCQCh. 5 - Prob. 26MCQCh. 5 - Prob. 27MCQCh. 5 - Prob. 8SGRCh. 5 - Prob. 19SGRCh. 5 - Prob. 27SGRCh. 5 - Prob. 28SGRCh. 5 - Prob. 29SGRCh. 5 - Prob. 31SGRCh. 5 - Prob. 32SGRCh. 5 - Prob. 33SGRCh. 5 - Prob. 34SGRCh. 5 - Prob. 35SGRCh. 5 - Prob. 36SGRCh. 5 - Prob. 37SGRCh. 5 - Prob. 38SGRCh. 5 - Prob. 39SGRCh. 5 - Prob. 40SGRCh. 5 - Prob. 42SGRCh. 5 - Prob. 43SGRCh. 5 - Prob. 45SGRCh. 5 - Prob. 1PTCh. 5 - Prob. 2PTCh. 5 - Prob. 3PTCh. 5 - Prob. 4PTCh. 5 - Prob. 5PTCh. 5 - Prob. 6PTCh. 5 - Prob. 7PTCh. 5 - Prob. 8PTCh. 5 - Prob. 9PTCh. 5 - Prob. 10PTCh. 5 - Prob. 11PTCh. 5 - Prob. 12PTCh. 5 - Prob. 13PTCh. 5 - Prob. 14PTCh. 5 - Prob. 17PTCh. 5 - Prob. 18PTCh. 5 - Prob. 25PTCh. 5 - Prob. 26PTCh. 5 - Prob. 1STPCh. 5 - Prob. 2STPCh. 5 - Prob. 3STPCh. 5 - Prob. 4STPCh. 5 - Prob. 5STPCh. 5 - Prob. 6STPCh. 5 - Prob. 7STPCh. 5 - Prob. 8STPCh. 5 - Prob. 9STPCh. 5 - Prob. 10STPCh. 5 - Prob. 11STPCh. 5 - Prob. 12STPCh. 5 - Prob. 13STPCh. 5 - Prob. 14STPCh. 5 - Prob. 15STPCh. 5 - Prob. 16STPCh. 5 - Prob. 17STP
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- The X is a variable in the picture, not a multiplication sign. After the variables the number is a power like X to the power of 9 Could I get assistance on how to solve this problem?arrow_forwardhow to do question 10 where u have to graph and then find domain and range. 10. y= 4x^2+24x+13arrow_forwardUse a . Venn Diagram (Euler Diagram) or truth table to decide whether each argument is valid or invalid Some of these kids are rude. Jimmy is one of these kids. Therefore, Jimmy is rude! Premise: Some of the kids are rude. Premise: Jimmy is one of these kids. Conclusion: Jimmy is rude! I dont have an image. Do you reallly need one?arrow_forward
- The functions f(x) = x² - 3 and g(x) = x² + 2 are shown on the graph. + N y 10 LO 5 f(x) = x² - 3 4 ♡ -3 -2 -10 -1 -2 -4- -5 x 2 3 4 56 7 8 9 g(x) = x² + 2 If the equations were changed to the inequalities shown, explain how the graph would change. y≤ x² - 3 y>-x²+2arrow_forwarda) find two linear map f. 9: R² →R³ s-t (1-5)=(1,-5)=(2, 2,0) b) let f: RR linear map set (3)=-\ find (√5) and (√7) f (-1) c) let X be Vector space over R and let sig ex difcid h: X-R³ s.t h(x)=(f(x),0,9(x)) xex Prove that his linear map- d) let f = L(x) S-t f²+2f+1=0 find §. e) find ker(s) s-t SiR³ R² = f(x, y, z)=(2x+1). ******arrow_forwardA craftsman of string instruments has received a new order to craft violins and guitars. The craftsman haslimited resources (wood, string, varnish) and time available to create the instruments. Each type of instrument(violin and guitar) requires specific amounts of these resources as well as a certain amount of time to complete.The craftsman wants to find the optimal number of violins and guitars to create in order to maximize the profitfrom selling them, while respecting the resource and time constraints (all instruments will be sold).The profit from selling each violin is 6,000 NOK, and the profit from selling each guitar is 3,000 NOK.Each violin requires 4 kg of wood, 0.3 l of varnish, and 2 m of string, and takes 3 days to craft. For eachguitar, the craftsman needs 5 kg of wood, 0.1 l of varnish, and 6 m of string, and it takes 2 days to make it.The craftsman’s workshop is stocked with 60 kg of wood, 2.5 l of varnish, and 65 m of string. The order needsto be completed in 30…arrow_forward
- C Clever | Portal x ALEKS - Marisa Haskins - Le Marisa Haskins - Essay Temp x Earth and Space 2 Desmos | Graphing Calculator x cwww-awy.aleks.com/alekscgi/x/Isl.exe/10_u-IgNslkr7j8P3JH-IQ2_KWXW3dyps2nJxZ_kvzXfsB26H8ZG13mFzq9lmGAYN JJOEyt0CsUr4AMXmcIVNqw-dNsEi_PzyC7v ◇ Exponents and Exponential Functions Finding the final amount in a word problem on compound interest 0/5 Ma John deposited $4000 into an account with 4.6% interest, compounded annually. Assuming that no withdrawals are made, how much will he have in the account after 7 years? Do not round any intermediate computations, and round your answer to the nearest cent. $0 Explanation Check 1 ! 12 Q W # 3 品: S חח E $ SA 4 4 a R 5775 % e MacBook Air ৫ Di F6 DD ©2025 McGraw Hill LLC. All Rights Reserved. Terms of Use Privacy Center Accessi 8 * ∞ & 27 Λ <6 T Y U DII DD FB 8° - A 1 2 小 F10 F11 ) ) 9 0 יו 0 P {arrow_forwardfor B in question 2, the inner product Is the picture given alonearrow_forward2. Assume that ƒ: R100 R² is linear and that for certain u, ER100 f(u) = - (4) and ƒ(v) = (2). Explicitly compute with work the following: (a). (b) (c) f(u+v) f(100) Assume that W is a vector space and g,h: W → R are both linear maps. Show that the function k : W→ R², k(w) = (()) is linear.arrow_forward
- 6 5 4 3 T 2 له 1- 1 -10-9 -8 -7 -6 -4 -3 -2 -1 0 2 3 4 5 -1- -2 -3 -4 -5. -8 -9. Which system is represented in the graph? Oy > x²+4x-5 y>x+5 Oy x²+4x-5 yarrow_forwardThe functions f(x) = x² - 3 and g(x) = x² + 2 are shown on the graph. + N y 10 LO 5 f(x) = x² - 3 4 ♡ -3 -2 -10 -1 -2 -4- -5 x 2 3 4 56 7 8 9 g(x) = x² + 2 If the equations were changed to the inequalities shown, explain how the graph would change. y≤ x² - 3 y>-x²+2arrow_forwardThe function f(x) is shown in the graph. 2 1 y -1 0 1 2 3 4 5 -1- -3. f(x) -4 -5 -6. Which type of function describes f(x)? ○ Exponential O Logarithmic ○ Rational O Polynomial .co. 6 7arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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GCSE Maths - What are Inequalities? (Inequalities Part 1) #56; Author: Cognito;https://www.youtube.com/watch?v=e_tY6X5PwWw;License: Standard YouTube License, CC-BY
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