Question

How would I check if 3(6 + 5y) = 2(-5 + 4y) and y = -4 are equivalent?

A) Substitute y = -4 into both equations and check if they are equal.
B) Simplify both equations and compare the results.
C) Use the distributive property to check if both sides are equal.
D) Cross-multiply and compare the results.

Answer 1

To determine if 3(6 + 5y) = 2(-5 + 4y) and y = -4 are equivalent, substitute y = -4 into both sides of the equation and simplify to see if they are equal. In this case, both sides simplify to -42, indicating the equations are equivalent for y = -4.

Step-by-step explanation:

To check if the equation 3(6 + 5y) = 2(-5 + 4y) is equivalent to y = -4, you should substitute y = -4 into both sides of the equation and check if they are equal. This process aligns with option A: Substitute y = -4 into both equations and check if they are equal. Here's how you can do it step by step:

1. Substitute y = -4 into the left side of the first equation: 3(6 + 5(-4)).
2. Simplify the expression: 3(6 - 20) becomes 3(-14), which simplifies further to -42.
3. Substitute y = -4 into the right side of the first equation: 2(-5 + 4(-4)).
4. Simplify the expression: 2(-5 - 16) becomes 2(-21), which simplifies further to -42.
5. Compare the two results: Since both sides equal -42 when y is -4, the two equations are equivalent for this value of y.