Question

1. write an \x\ in the box beside each expression that is equivalent to -6 - (1.25 + 3.5). select all that apply.

□ (-6 - 1.25) + 3.5
□ -3.5 + (-6 - 1.25)
□ (-6 - 1.25) - 3.5
□ 3.5 + (-6 - 1.25)
□ -(6 + 1.25) + 3.5
□ -(3.5 - 6) - 1.25
□ -(6 + 1.25) - 3.5

Explanation:

First, simplify the original expression: \(-6 - (1.25 + 3.5) = -6 - 1.25 - 3.5\) (by distributing the negative sign).

Step 1: Analyze \((-6 - 1.25) + 3.5\)

Simplify: \(-6 - 1.25 + 3.5\). Not equivalent to \(-6 - 1.25 - 3.5\).

Step 2: Analyze \(-3.5 + (-6 - 1.25)\)

Rearrange: \(-6 - 1.25 - 3.5\). Equivalent.

Step 3: Analyze \((-6 - 1.25) - 3.5\)

Simplify: \(-6 - 1.25 - 3.5\). Equivalent.

Step 4: Analyze \(3.5 + (-6 - 1.25)\)

Rearrange: \(-6 - 1.25 + 3.5\). Not equivalent.

Step 5: Analyze \(-(6 + 1.25) + 3.5\)

Simplify: \(-6 - 1.25 + 3.5\). Not equivalent.

Step 6: Analyze \(-(3.5 - 6) - 1.25\)

Simplify: \(-3.5 + 6 - 1.25 = 6 - 3.5 - 1.25\). Not equivalent.

Step 7: Analyze \(-(6 + 1.25) - 3.5\)

Simplify: \(-6 - 1.25 - 3.5\). Equivalent.

Answer:

The expressions equivalent to \(-6 - (1.25 + 3.5)\) are:

• \(\boldsymbol{-3.5 + (-6 - 1.25)}\)
• \(\boldsymbol{(-6 - 1.25) - 3.5}\)
• \(\boldsymbol{-(6 + 1.25) - 3.5}\)