Question

Find all equivalent expressions. 10-8(4x-2)

A 10- 32x + 16
B-32x + 26
C. 4(2x-1)
D-2(6x + 5)
E2(-16x + 13)

Answer 1

The expressions equivalent to 10 - 8(4x - 2) are found by applying the distributive property and simplifying, resulting in 26 - 32x. The equivalent expressions among the options provided are A, B, and E.

Step-by-step explanation:

The student is asked to find all expressions equivalent to 10 - 8(4x - 2). To find the equivalent expressions, we need to apply the distributive property of multiplication over subtraction, which involves multiplying -8 with both 4x and -2 inside the parentheses, and then combine any like terms.

Let's simplify the original expression step by step:

1. Multiply -8 by 4x to get -32x.
2. Multiply -8 by -2 to get +16.
3. Combine the multiplication results with the original 10, we get 10 + 16 - 32x.
4. Simplify further by adding 10 and 16 to get 26 - 32x.

Now, let's examine the provided options to see which are equivalent to the simplified expression, 26 - 32x:

• A: 10 - 32x + 16 is equivalent after rearranging and combining like terms.
• B: -32x + 26 is directly equivalent to our simplified expression.
• C: 4(2x - 1) is not equivalent because when expanded, it becomes 8x - 4, which doesn’t match our simplified expression.
• D: -2(6x + 5) is not equivalent because when expanded, it becomes -12x - 10, which doesn’t match our simplified expression.
• E: 2(-16x + 13) is not equivalent because when expanded, it becomes -32x + 26, which is indeed equivalent to our expression.

Therefore, the equivalent expressions to 10 - 8(4x - 2) are options A, B, and E.