To solve the equation [tex]\(-\frac{3}{2} x = 22\)[/tex], we need to isolate [tex]\(x\)[/tex]. We will go through this step-by-step.
### Step 1: Isolate [tex]\(x\)[/tex]
The equation is:
[tex]\[
-\frac{3}{2} x = 22
\][/tex]
To eliminate the fraction, we can multiply both sides of the equation by the reciprocal of [tex]\(-\frac{3}{2}\)[/tex], which is [tex]\(-\frac{2}{3}\)[/tex]:
[tex]\[
x = 22 \cdot -\frac{2}{3}
\][/tex]
### Step 2: Multiply to Solve for [tex]\(x\)[/tex]
Multiply the right-hand side:
[tex]\[
x = 22 \cdot -\frac{2}{3}
\][/tex]
Breaking it down:
[tex]\[
22 \cdot -\frac{2}{3} = 22 \cdot -\frac{2}{3} = \frac{22 \cdot -2}{3} = \frac{-44}{3}
\][/tex]
### Step 3: Simplify the Expression
Now perform the division:
[tex]\[
\frac{-44}{3} = -14.6666666666667
\][/tex]
### Final Solution
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation [tex]\(-\frac{3}{2} x = 22\)[/tex] is:
[tex]\[
x = -14.6666666666667
\][/tex]
