Question

An equation is shown below: 8x + 2(x - 7) = 7x + 3x - 14 Part A: Solve the equation and write the number of solutions. Show all the steps. Part B: Name one property you used to solve this equation.

Answer 1

`8x+2(x-7)=7x+3-14\\8x+2x-14=7x+3-14~~Distributive~property\\10x-14=7x-11~combine~like~terms\\ 3x-14=-11~subtract~the~7x~from~both~sides\\ 3x=3~add~14~to~both~sides\\x=1~divide~both~sides~by~3`

Answer 2

A) there are infinite solutions.

B) distributive property of multiplication

Explanation:

Given the equation:

8x + 2(x - 7) = 7x + 3x - 14

To solve this, first apply the distributive property of multiplication,

8x + 2x - 14 = 7x + 3x - 14

Then, combine the similar terms,

8x + 2x -7x -3x = -14 + 14

0 = 0

This means that any value of x satisfy the equation, that is, there are infinite solutions.