To solve the equation [tex]\(\frac{3}{4} x = -8\)[/tex] for [tex]\(x\)[/tex], we need to isolate [tex]\(x\)[/tex].
Start with the original equation:
[tex]\[ \frac{3}{4} x = -8 \][/tex]
To isolate [tex]\(x\)[/tex], we should multiply both sides of the equation by the reciprocal of [tex]\(\frac{3}{4}\)[/tex], which is [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[ \frac{4}{3} \left( \frac{3}{4} x \right) = \frac{4}{3} \left( -8 \right) \][/tex]
On the left-hand side, the [tex]\(\frac{4}{3}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex] will cancel each other out, leaving us with:
[tex]\[ x = \frac{4}{3} \cdot (-8) \][/tex]
Simplify the right-hand side:
[tex]\[ x = -8 \cdot \frac{4}{3} \][/tex]
Therefore, the equation showing the correct one-step solution is:
[tex]\[ \frac{4}{3}\left(\frac{3}{4}\right) x = -8\left(\frac{4}{3}\right) \][/tex]
