Sure, let's solve the given equation step by step.
We start with the equation:
[tex]\[
-\frac{2}{3} x - \frac{21}{4} = \frac{27}{4}
\][/tex]
### Step 1: Eliminate the constant term on the left side.
We add [tex]\(\frac{21}{4}\)[/tex] to both sides of the equation to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
-\frac{2}{3} x - \frac{21}{4} + \frac{21}{4} = \frac{27}{4} + \frac{21}{4}
\][/tex]
Simplifying the left side, we have:
[tex]\[
-\frac{2}{3} x = \frac{27}{4} + \frac{21}{4}
\][/tex]
### Step 2: Simplify the right-hand side.
Combine the fractions on the right side:
[tex]\[
- \frac{2}{3} x = \frac{27 + 21}{4}
\][/tex]
[tex]\[
- \frac{2}{3} x = \frac{48}{4}
\][/tex]
[tex]\[
- \frac{2}{3} x = 12
\][/tex]
### Step 3: Solve for [tex]\(x\)[/tex] by multiplying both sides by the reciprocal of [tex]\(-\frac{2}{3}\)[/tex].
The reciprocal of [tex]\(-\frac{2}{3}\)[/tex] is [tex]\(-\frac{3}{2}\)[/tex]. Thus, we multiply both sides by [tex]\(-\frac{3}{2}\)[/tex]:
[tex]\[
x = 12 \times \left(-\frac{3}{2}\right)
\][/tex]
Calculating the right side, we get:
[tex]\[
x = -18
\][/tex]
Thus, the solution to the equation is:
[tex]\[
x = -18
\][/tex]
