### Solving the Equation 5x + 2 = 2x + 17Solve the equation $ 5x + 2 = 2x + 17 $ in two ways: with equations and with math drawings of a pan balance. Relate the two methods.#### Method 1: Solving with Equations1. Start with the given equation: \[ 5x + 2 = 2x + 17 \]2. Subtract $ 2x $ from both sides to isolate terms with $ x $ on one side: \[ 5x - 2x + 2 = 2x - 2x + 17 \] \[ 3x + 2 = 17 \]3. Subtract 2 from both sides: \[ 3x + 2 - 2 = 17 - 2 \] \[ 3x = 15 \]4. Divide both sides by 3 to solve for $ x $: \[ \frac{3x}{3} = \frac{15}{3} \] \[ x = 5 \]So, the solution to the equation is $ x = 5 $.#### Method 2: Solving with a Pan Balance DiagramIn a pan balance diagram, each side of the balance represents one side of the equation. 1. **Create the initial balance:** - On the left side of the pan balance, represent $ 5x + 2 $. - On the right side of the pan balance, represent $ 2x + 17 $.2. **Balance the equation:** - To balance the representation, remove $ 2x $ from both sides to simplify it, just as in the algebraic solution. - This leaves $ 3x + 2 $ on the left pan and $ 17 $ on the right pan.3. **Adjust for constants:** - Subtract 2 units from both sides to maintain balance, resulting in $ 3x $ on the left pan and $ 15 $ on the right pan.4. **Determine the variable value:** - Each group of $ x $ on the left pan collectively balances with

Answered: Solve 5x+2=2x+17 in two ways: with…

Math

Algebra

Solve 5x+2=2x+17 in two ways: with equations and with math drawings of a pan balance. Relate the two methods.

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter5: Factoring Polynomials

Section5.13: Using Factoring To Solve Problems

Problem 14P

See similar textbooks

Related questions

Q: 31. What time after 7:00 o'clock will the hands of the clock be 65° amapart, for the first time? ww…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Let f(x) = x² and g(x) = sinx. The composite function (fog)(x) is equal to B. x² sin(x) C. (sin(x))²…

A: f(x)= x2 and g(x) = sinx Find f(g(x))

Q: Find the logarithm. log 82

Q: Ahmed and Rami are finding the surface area of a cylinder with a height of 7 cm and a radius of 10…

A: Here is the solution.

Q: Consider the following. T is the clockwise rotation (0 is negative) of 60° in R2, v = (1, 6). (a)…

A: Solution

Q: 10 [19] 2 0 1 18. Compute (ATBT) - BA, if A = and B = 0 1 A [1¹] B. 0 0 -5 4 1 19. Find C(AB), if A…

Q: A city's population in the year 1957 was 1,555,300 people. In 1987, the population was 1,558,300…

A: Solved below.

Q: Some screws are being used to set up the conveyor belt. [Hint: Lesson 3.3] a) The workers currently…

A: Given problem:- Some screws are being used to set up the conveyor belt. a) The workers currently…

Q: vertical

Q: Prove Bernouilli’s Inequality which states: If x ≥ −2 then (2+ x)n ≥ 1 + nx for all natural numbers…

Q: For each, steps 1-5 are the same for each part so only show once then show the final answer with…

Q: Many doctors rely on the use of intravenous medication administration in order to achieve an…

A: Domain:- The set of points x∈ℝ such the function at x exits.See below the answer and calculation

Q: Suppose that the functions and s are defined for all real numbers x as follows. r r(x)=x-6 s(x) =…

Q: If f(x) =........, then f(x) is irreducible in Z7[x]. (i) x³ + 2 x² + 2x + 1 3 Option 1 (ii) x² + 3…

Q: Use a calculator to complete the following table to five decimal places. n 10 100 1,000 10,000…

A: I am going to solve the problem by using some simple algebra to get the required result of the given…

Q: If cotx = D. cos x = Z. and x is in quadrant II, then A. sinx || ! B. cos x C. sin a CTLA

A: follow next step

Q: 1 f(x)=5; find lim f(x) and lim f(x) X→∞0 x→0 Choose the correct graph below. O A. B. O C. Find lim…

A: Topic = Functions

Q: Q5: find the possible solutin area: Max Z= 8x+ 6Y S.To 2X+ 2Y ≤60 2X +4Y ≤ 48 X,Y20

A: To find the solution we have to plot the constraints. Here we use the graphing tools to find the…

Q: Find the domain and range. y=√16-x²

A: Topic = Functions Domain x∈-4,4 range y∈0,4

Q: Find the values of a) Ln(1-i) b) Ln (3+√3)

Q: Calculate 1+2+3+...+500 by finding and evaluating another expression that equals this sum. Explain…

A: Solve the following

Q: Find (A) the derivative of F(x)S(x) without using the product rule, and (B) F'(x)S'(x). Note that…

Q: 14. Prove that (1- cos x) csc x = 1

Q: Evaluate c – 3d when c = 1 and d = 1/3

A: evaluate c -3d c = 1 d = 1/3 here basic substraction is apply and we get answer put the value of…

Q: Build the least common multiple of A, B, and C using the example/method in module 8 on page 59860.…

Q: 12 16. A) Determine the primary ratios for tan A = - in the second quadrant. - 5 B) Determine the…

Q: A) (1 + √₂)² B) (1 -√2)² c)(1+√2)(1+√-2) D)(1+√2)(1-√√2) E)√2² + (√2)² Which of the above…

A: A) 1+22B) 1-22C) 1+21+2D) 1+21-2E) 22+22

Q: 5. The graph of y = f(x) is shown. a) Evaluate f(4). b) Determine the amplitude. c) Determine the…

A: Sinusoidal curve

Q: Write the quadratic equation whose roots are -6 and 4, and whose leading coefficient is 2. (Use the…

A: Topic = Quadratic equation

Q: Here is a Venn diagram showing the sets A, B, and C, as well as the universal set U. -B 8 S h,p X…

Q: Mary Branson invested her summer earnings of $2000 in a savings account for college. The account…

Q: Write two word problems for 300 / 12 , one for each of the two interpretations of division.

A: Solution of given question is written in below steps.

Q: 1 f(x) = 1 X+1 a.) Identify all int's (ONE it does not exist.) X-int (x, y) = (x₁y) = ( 3 y-int…

Q: If D is a ring of integers module 13. Then rad (D) {0}.

A: given

Q: Differentiate the following function. f(x) = -3+3x+5ex

Q: Solve a real-life working example of Newton's forward interpolation method, take random 5 values for…

Q: Line 1 passes through the point (4, 0) and is perpendicular to the line y - 2x + 3. Line 2 passes…

A: (a) To find the equation of two lines: (b) To find the point of intersection:

Q: An international company has 25,100 employees in one country. If this represents 16.8% of the…

A: We can solve the given problem by using the concept of percentage.

Q: The total sales of S (in thousands of DVD's) of a certain movie are given by the following formula…

Q: Here is the graph of a polynomial function with degree 4. Select all of the statements that are true…

A: Given, Graph

Q: Find (if possible) the rational zeros of the function. (Enter your answers as a comma-separated…

Q: Prove that if ACB, then A-B=0.

A: This question can be solved using the concept of set theory.

Q: Simplify the function algebraically and find the limit. 2 x + 6x-7 lim 2 x→1x - 2x + 1 Select the…

A: Using L-hospital rule for 0/0 forms

Q: (f) Solve the following equation, checking that your solution is correct: 24 72 9-xx+3

A: calculation of above requirement are as follows

Q: use dimensional analysis to convert the given unit to the unit indicated. Where necessary, round…

A: The given dimension, 40,000 ft3

Q: Solve for r to two decimal places. 4= e 5r ra (Do not round until the final answer. Then round to…

A: Topic = Algebra

Q: 22lnx 1. Evaluate definite integral for y = = √²² ¹nx dx X

A: we havey=∫122lnx xdx

Q: If the exponential parent function, f(x) = 3x is reflected across the y-axis and then translated…

Q: Hideki is draining a 45 gallon aquarium at a rate of 15 gallons per minute what is the initial value…

A: This question is related to linear function, we will solve it using given information.

Q: 1. A ball fits perfectly inside of a 6-inch cube. What is the volume of the ball in cubic inches?

Question

### Solving the Equation 5x + 2 = 2x + 17

Solve the equation $ 5x + 2 = 2x + 17 $ in two ways: with equations and with math drawings of a pan balance. Relate the two methods.

#### Method 1: Solving with Equations

1. Start with the given equation:
\[
5x + 2 = 2x + 17
\]

2. Subtract $ 2x $ from both sides to isolate terms with $ x $ on one side:
\[
5x - 2x + 2 = 2x - 2x + 17
\]
\[
3x + 2 = 17
\]

3. Subtract 2 from both sides:
\[
3x + 2 - 2 = 17 - 2
\]
\[
3x = 15
\]

4. Divide both sides by 3 to solve for $ x $:
\[
\frac{3x}{3} = \frac{15}{3}
\]
\[
x = 5
\]

So, the solution to the equation is $ x = 5 $.

#### Method 2: Solving with a Pan Balance Diagram

In a pan balance diagram, each side of the balance represents one side of the equation.

1. **Create the initial balance:**
- On the left side of the pan balance, represent $ 5x + 2 $.
- On the right side of the pan balance, represent $ 2x + 17 $.

2. **Balance the equation:**
- To balance the representation, remove $ 2x $ from both sides to simplify it, just as in the algebraic solution.
- This leaves $ 3x + 2 $ on the left pan and $ 17 $ on the right pan.

3. **Adjust for constants:**
- Subtract 2 units from both sides to maintain balance, resulting in $ 3x $ on the left pan and $ 15 $ on the right pan.

4. **Determine the variable value:**
- Each group of $ x $ on the left pan collectively balances with

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

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

Where is the pan balance drawing to represent this equation and relate the math equations to the drawing?

Solution

by Bartleby Expert

SEE SOLUTION