Question

8x + 2(x − 7) = 7x + 3x − 14

Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points)

Part B: Name one property you used to solve this equation. (4 points)

Answer 1

hope it helps you!!!!!!!!!!!!!!

Answer 2

Start with

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

Apply the distributive property to expand the left hand side:

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

Sum like terms:

$10x-14=10x-14$

Apply the additive property of equality to add 14 to both sides:

$10x=10x$

Apply the additive property of equality to subtract 10x to both sides:

$0=0$

This means that the equation was actually an identity, i.e. the left and right hand sides were actually the same expression.

Since they are the same expression, it doesn't matter which values you plug into x, it will always be a solution of this equation.

Solution: infinite. All numbers are solutions of this equation.

Property used: Listed while solving the equation.