Question

1. jayda was trying to solve the equation 9x + 4 - 3x = 10x - 7. the first step she took left her with the equation 9x + 11 - 3x = 10x. which of the following properties did she use to take that step? (a) she correctly used the equality property of multiplication (b) she incorrectly used the equality property of multiplication (c) she correctly used the equality property of addition (d) she incorrectly used the equality property of addition 8. which of the equations below has one - solution? circle all that apply. (a) 3x - 7x=-4x (b) 3x - 7x + 3=-2x - 4 - 2x (c) 7x + 4 = 6x + 4 (d) 9x - 7 = 3x + 2x - 7 (e) 7x - 4=-7x - 4

Explanation:

Step1: Simplify the left - hand side of the equation

Combine like terms in $9x + 11-3x$. We have $9x-3x+11 = 6x + 11$. The original equation $9x + 11-3x=10x$ becomes $6x + 11=10x$.

Step2: Analyze the operation used in the first step

The first step Jayda took was combining like - terms $9x$ and $-3x$. This is an application of the addition property of equality (since we are adding the coefficients of the like terms $9x$ and $-3x$). In the process of combining $9x$ and $-3x$ to get $6x$, we are essentially performing addition of the coefficients $9+( - 3)=6$.

Answer:

a. She correctly used the equality property of addition.