To solve the equation [tex]\(\frac{3}{4}x - 1.72 = -6.82\)[/tex], follow these detailed, step-by-step instructions:
1. The first step is to add 1.72 on both sides. This helps to isolate the term with [tex]\(x\)[/tex].
[tex]\[
\frac{3}{4}x - 1.72 + 1.72 = -6.82 + 1.72
\][/tex]
Simplifying both sides, we get:
[tex]\[
\frac{3}{4}x = -5.10
\][/tex]
2. The second step is to multiply by the reciprocal of [tex]\(\frac{3}{4}\)[/tex] on both sides. The reciprocal of [tex]\(\frac{3}{4}\)[/tex] is [tex]\(\frac{4}{3}\)[/tex].
[tex]\[
\left(\frac{4}{3}\right) \cdot \frac{3}{4}x = -5.10 \cdot \left(\frac{4}{3}\right)
\][/tex]
Simplifying, we get:
[tex]\[
x = -6.8
\][/tex]
Therefore, the solution is [tex]\( x = -6.8 \)[/tex].
