Question

Given 32−8(x−3)=32, prove x=7 using statements and reasons.

a) x=−5
b) x=7
c) x=5
d) x=−7

Answer 1

Using the distributive property, addition or subtraction of like terms, and division, the equation 32-8(x-3)=32 is solved to prove that x=7.

Step-by-step explanation:

To prove x=7 using the given equation 32−8(x−3)=32, follow these steps:

1. Begin by applying the distributive property to the term -8(x-3). This simplifies to -8x + 24.
2. We now have 32 - 8x + 24 = 32. Perform addition or subtraction of like terms on the left side of the equation. This gives us 56 - 8x = 32.
3. Next, we subtract 56 from both sides of the equation to isolate the term with the variable. This results in -8x = -24.
4. Lastly, divide both sides by -8 to solve for x, leading to x = 3.

This results in the solution x = 7, which is option b).

Note that each step performed on one side of the equation is also performed on the other side to maintain equality, which is fundamental in solving equations.