Sure, let's solve the equation [tex]\(-\frac{4}{3} x = \frac{1}{7}\)[/tex] step by step.
1. Write down the given equation:
[tex]\[
-\frac{4}{3} x = \frac{1}{7}
\][/tex]
2. Isolate [tex]\(x\)[/tex]: To isolate [tex]\(x\)[/tex], we need to get rid of the coefficient [tex]\(-\frac{4}{3}\)[/tex] that is multiplied by [tex]\(x\)[/tex]. We do this by multiplying both sides of the equation by the reciprocal of [tex]\(-\frac{4}{3}\)[/tex].
3. Find the reciprocal: The reciprocal of [tex]\(-\frac{4}{3}\)[/tex] is [tex]\(-\frac{3}{4}\)[/tex].
4. Multiply both sides by the reciprocal:
[tex]\[
x = \left(-\frac{3}{4}\right) \cdot \frac{1}{7}
\][/tex]
5. Multiply the fractions: When multiplying fractions, multiply the numerators together and the denominators together:
[tex]\[
x = \frac{-3 \cdot 1}{4 \cdot 7} = \frac{-3}{28}
\][/tex]
Therefore, the solution to the equation is:
[tex]\[
x = -\frac{3}{28}
\][/tex]
