**Graphing the Solution of the Inequality on a Number Line**To graph the solution of the inequality $2x - (3 - x) > x + 1$ on the number line, follow these steps.### Step 1: Simplify the InequalityFirst, simplify the inequality to find a simpler form.\[ 2x - (3 - x) > x + 1 \]Distribute the negative sign:\[ 2x - 3 + x > x + 1 \]Combine like terms:\[ 3x - 3 > x + 1 \]Subtract $x$ from both sides:\[ 2x - 3 > 1 \]Add 3 to both sides:\[ 2x > 4 \]Divide both sides by 2:\[ x > 2 \]### Step 2: Represent the Solution on a Number LineThe inequality $x > 2$ is represented on the number line as an open circle at 2 and shading to the right to indicate all values greater than 2.### Step 3: Correct GraphInspect the given options and select the one that matches the solution:- **Option A**: Shows a closed circle at 2 with shading to the left, which would represent $x \leq 2$.- **Option B**: Shows an open circle at -1 with shading to the right, which represents $x > -1$.- **Option C**: Shows an open circle at -1 with shading to the left, which represents $x < -1$.- **Option D**: Shows an open circle at 2 with shading to the right, which accurately represents $x > 2$.Therefore, the correct graph for the solution $x > 2$ is **Option D**.### Visual AidsEach option contains a number line ranging from -5 to 5, with circles and shaded regions indicating different ranges of solutions:- **Closed Circle**: Indicates the number is included in the solution.- **Open Circle**: Indicates the number is not included in the solution.- **Shading**: Direction of the shading (left or right) shows whether the solution includes numbers less than or greater than the circled number.This approach helps visualize the range of values that satisfy the inequality, making abstract algebraic concepts easier to understand.

To graph the solution of given inequality 2x-(3-x)>x+1 on the number line.

Graph the solution of the inequality 2x – (3 – x) > x + 1 on the number line. O A. + -5 -4 -3 -2 -1 0 1 2 3 4 5 O B. + ++O+ -5 -4 -3 -2 -1 0 1 2 3 4 C. +++O -5 -4 -3 -2 -1 0 1 2 O D. ++ -5 -4 -3 -2 -1 0 1 2 3 +0I+ 4 5 4. 3.

Graph the solution of the inequality 2x – (3 – x) > x + 1 on the number line. O A. + -5 -4 -3 -2 -1 0 1 2 3 4 5 O B. + ++O+ -5 -4 -3 -2 -1 0 1 2 3 4 C. +++O -5 -4 -3 -2 -1 0 1 2 O D. ++ -5 -4 -3 -2 -1 0 1 2 3 +0I+ 4 5 4. 3.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: which inequality is equivalent to 3(7+4) - 8(t - 2) < 9t

A: Given: 3(7+4) - 8(t - 2) < 9t ⇒21+12-8t+16<9t⇒33-8t+16<9t⇒49-8t<9t⇒t<-49

Q: Betsy entered the expression z + 6z included in the solution set for the inequality z+ 6z -7<-127 7…

Q: Graph the inequality on the axes below. 3 y > х — 1 - 3 |2

A: The given inequality can be graphed by first drawing the line and then testing any point in the x-y…

Q: Which quadratic inequality is graphed below? a. y≥ (x-2)(x+3) b. y>(x-2)(x+3) C. y> (x+2)(x-3) d.…

Q: A student with P60 pocket money goes to buy some snacks in the canteen. He/she is looking forward to…

Q: X -2

Q: Find the solution of the inequality 7x-18 >10x-12?

A: We have given inequality 7x-18 >10x-12 -18>10x-7x-12 -18+12>3x -6>3x -63>x -2>x…

Q: Solve. Write the solution set in interval notation. Show all work -4x + 9(x – 5) + 20 < 5(x – 6) +7

A: Given: -4x + 9(x-5) +20 ≤5(x-6) +7

Q: Which graph shows the solution set of the inequality -2(2x + 3) < 26? A. -8 -6 -2 0 2 4 В. -8 -6 4 2…

Q: Determine the largest subset of real numbers that is NOT a solution to the inequality (x+ 8)(x−7) >…

Q: Graph the solution to the inequality on the numnber line. 2x-6 > 14

Q: Use the graph to solve forx if 2*+2 > -4x2 – 8x + 4

Question

**Graphing the Solution of the Inequality on a Number Line**

To graph the solution of the inequality $2x - (3 - x) > x + 1$ on the number line, follow these steps.

### Step 1: Simplify the Inequality
First, simplify the inequality to find a simpler form.

\[ 2x - (3 - x) > x + 1 \]

Distribute the negative sign:

\[ 2x - 3 + x > x + 1 \]

Combine like terms:

\[ 3x - 3 > x + 1 \]

Subtract $x$ from both sides:

\[ 2x - 3 > 1 \]

Add 3 to both sides:

\[ 2x > 4 \]

Divide both sides by 2:

\[ x > 2 \]

### Step 2: Represent the Solution on a Number Line
The inequality $x > 2$ is represented on the number line as an open circle at 2 and shading to the right to indicate all values greater than 2.

### Step 3: Correct Graph
Inspect the given options and select the one that matches the solution:

- **Option A**: Shows a closed circle at 2 with shading to the left, which would represent $x \leq 2$.
- **Option B**: Shows an open circle at -1 with shading to the right, which represents $x > -1$.
- **Option C**: Shows an open circle at -1 with shading to the left, which represents $x < -1$.
- **Option D**: Shows an open circle at 2 with shading to the right, which accurately represents $x > 2$.

Therefore, the correct graph for the solution $x > 2$ is **Option D**.

### Visual Aids
Each option contains a number line ranging from -5 to 5, with circles and shaded regions indicating different ranges of solutions:
- **Closed Circle**: Indicates the number is included in the solution.
- **Open Circle**: Indicates the number is not included in the solution.
- **Shading**: Direction of the shading (left or right) shows whether the solution includes numbers less than or greater than the circled number.

This approach helps visualize the range of values that satisfy the inequality, making abstract algebraic concepts easier to understand.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Inequality$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

Which number line shows the solution to the inequality -2(3x – 1) < 8? O . + + + + + + -5 -4 -3 -2 -1 1 2 3 4 O B. +0+ + + -5 -4 -3 -2 -1 1 2 4 O . + + +0+ + -5 -4 -3 -2 -1 1 4 OD. + + ++ ++0 + + -5 -4 -3 -2 -1 1 4 LO 3. 3. 3.
Which of the following are solutions to the inequality, (8x − 16) + 4x − 2 > 15 ? ☐ ☐ ☐ ☐ 00 00|10 3.2 10 3 25 8 3.1 13 4
Graph the inequality on the axes below. 6x + 5y 2 -10 10 8. 6 5 4 -10 -9 -8 -7 -6 -4 -3 1 3 4 5 10 -5 -1 -1 -3 -4 -5 -6 -7 -8 -9 -10 S.uhmit Anruor
Which graph represents the solution to 2x + 4 < 2? A + -1 0 1 + -5 -4 -3 -2 2 3 4 5 B + + -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 + 4
Graph the inequality on the axes below. 5x + 4y > –32 10 8. 7 4 2 1 X. -10 -9 -8 -7 -6 -5 -4 -3 1 2 6. 8 -2 -1 3 4 7 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 6. 3.
Rolando drives at least 40 miles but less than 60 miles each week. A. Graph the compound inequality representing all of the possible distances Rolando could drive for 8 weeks. You may copy and paste the number line image into a document, use it to answer the question, save, then attach the image to this question. Rolando's Driving for 8 Weeks + 40 80 120 160 200 240 280 320 360 400 440 480 520 560 600 Miles Driven B. Explain why you chose to use the symbols you used for the endpoints of the compound inequality in part A. C. Rolando buys at least 8.5 but no more than 11 gallons of gas each week. The price of gas has ranged from $2.40 to $2.65 per gallon each week. Write an inequality to model all of the possible amounts of money (m) Rolando spends on gas each week. Show or explain all your work. Use the paperclip button below to attach files.
2.) A bakery has a fixed cost of $119.75 per day plus $2.25 for each pastry. The bakery would like to keep its dally costs at or below $500 per day. Which inequality shows the maximum number of pastries, p, that can be baked each day? A 2.25 +119.75p s 500 B (119.75 + 2.25)p s 500 C 119.75 + 2.25p s 500 D 2.25p-119.75 s 500 Solve the ineo find the maximum number of pastri to be baked each day. Answer pastries
Solve and graph the inequality and graph the solution. -2(4x- 14) < -10x + 12 十 (-00, -10) 217 -16 -15 -14 -13 -12 -11 -10 干 %+ -5 -4 -3 -9 -8 -7 -6 (-00, -8) %+ -1 キ -15 -14 -13 -12 -11 -10 -91 -8 -7 -6 -5 -4 -3 -2 (-8, 0) -15-14 -13 -12 -11 -10 -9 -8 -7 -- -5 -4 -3 -2 -1 (10, ) -9 -8 -7 -6 -5 -4 -17 -16 -15 -14 -13 -12 -11 -10
Graph the inequality on the axes below. x + 6y < 6 10 8 6. 5 3 2 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 6. 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10