To expand the expression [tex]\(-2\left(\frac{3}{4} x + 7\right)\)[/tex], you would use the distributive property. Here is how you would do it step-by-step:
1. Distribute the [tex]\(-2\)[/tex] to each term inside the parentheses:
[tex]\[
-2 \left(\frac{3}{4} x + 7\right) = -2 \cdot \left(\frac{3}{4} x\right) + (-2) \cdot 7
\][/tex]
2. Multiply [tex]\(-2\)[/tex] by [tex]\(\frac{3}{4} x\)[/tex]:
[tex]\[
-2 \cdot \left(\frac{3}{4} x\right) = -\frac{6}{4} x = -\frac{3}{2} x
\][/tex]
3. Multiply [tex]\(-2\)[/tex] by [tex]\(7\)[/tex]:
[tex]\[
-2 \cdot 7 = -14
\][/tex]
4. Combine the results:
[tex]\[
-\frac{3}{2} x - 14
\][/tex]
Therefore, the result of expanding [tex]\(-2\left(\frac{3}{4} x + 7\right)\)[/tex] using the distributive property is [tex]\(-\frac{3}{2} x - 14\)[/tex].
So, the property used to expand the expression is the distributive property.
