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Solve the two-step equation.

[tex]\[
-\frac{2}{3} x - \frac{21}{4} = \frac{27}{4}
\][/tex]

[tex]\[x = \square\][/tex]


Sagot :

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]