Answer :

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]