Question

1 select all expressions that are equivalent to $-3.75 + 2(-4x + 6.1) - 3.25x$. a $7x - 2x + 8.1$ b $8.45 - 8x - 3.25x$ c $-1.75 - 7.25x + 6.1$ d $-11.25x + 12.2 - 3.75$

Explanation:

Step1: Simplify the original expression

First, expand the term \(2(-4x + 6.1)\) using the distributive property \(a(b + c)=ab+ac\). So \(2(-4x + 6.1)=2\times(-4x)+2\times6.1=-8x + 12.2\). Then the original expression \(-3.75 + 2(-4x + 6.1)-3.25x\) becomes \(-3.75-8x + 12.2-3.25x\). Combine the constant terms: \(-3.75 + 12.2 = 8.45\), and combine the \(x\) terms: \(-8x-3.25x=-11.25x\). So the simplified original expression is \(8.45-11.25x\) (or \(-11.25x + 8.45\)).

Step2: Analyze Option A

Simplify option A: \(7x-2x + 8.1=5x + 8.1\). The coefficient of \(x\) is \(5\) and the constant term is \(8.1\), which is not equal to the simplified original expression (\(-11.25x + 8.45\)), so option A is not equivalent.

Step3: Analyze Option B

Simplify option B: \(8.45-8x-3.25x\). Combine the \(x\) terms: \(-8x-3.25x=-11.25x\), so the expression becomes \(8.45-11.25x\), which is the same as the simplified original expression. So option B is equivalent.

Step4: Analyze Option C

Simplify option C: \(-1.75-7.25x + 6.1\). Combine the constant terms: \(-1.75 + 6.1 = 4.35\), and the \(x\) term is \(-7.25x\). The expression is \(4.35-7.25x\), which is not equal to the simplified original expression, so option C is not equivalent.

Step5: Analyze Option D

Simplify option D: \(-11.25x + 12.2-3.75\). Combine the constant terms: \(12.2-3.75 = 8.45\), so the expression becomes \(-11.25x + 8.45\), which is the same as the simplified original expression. So option D is equivalent.

Answer:

B. \(8.45 - 8x - 3.25x\), D. \(-11.25x + 12.2 - 3.75\)