Solve for c 2/3*(c-18)=7

$\frac{2}{3} \cdot (c - 18) = 7$

Step 1

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} (\frac{2}{3} \cdot (c - 18)) = \frac{3}{2} \cdot 7$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} (\frac{2}{3} \cdot (c - 18))$ .

Apply the distributive property.

$\frac{3}{2} (\frac{2}{3} c + \frac{2}{3} \cdot - 18) = \frac{3}{2} \cdot 7$

Combine $\frac{2}{3}$ and $c$ .

$\frac{3}{2} (\frac{2 c}{3} + \frac{2}{3} \cdot - 18) = \frac{3}{2} \cdot 7$

Cancel the common factor of $3$ .

Factor $3$ out of $- 18$ .

$\frac{3}{2} (\frac{2 c}{3} + \frac{2}{3} \cdot (3 (- 6))) = \frac{3}{2} \cdot 7$

Cancel the common factor.

$\frac{3}{2} (\frac{2 c}{3} + \frac{2}{3} \cdot (3 \cdot - 6)) = \frac{3}{2} \cdot 7$

Rewrite the expression.

$\frac{3}{2} (\frac{2 c}{3} + 2 \cdot - 6) = \frac{3}{2} \cdot 7$

Multiply $2$ by $- 6$ .

$\frac{3}{2} (\frac{2 c}{3} - 12) = \frac{3}{2} \cdot 7$

Apply the distributive property.

$\frac{3}{2} \cdot \frac{2 c}{3} + \frac{3}{2} \cdot - 12 = \frac{3}{2} \cdot 7$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 c}{3} + \frac{3}{2} \cdot - 12 = \frac{3}{2} \cdot 7$

Rewrite the expression.

$\frac{1}{2} (2 c) + \frac{3}{2} \cdot - 12 = \frac{3}{2} \cdot 7$

Cancel the common factor of $2$ .

Factor $2$ out of $2 c$ .

$\frac{1}{2} (2 (c)) + \frac{3}{2} \cdot - 12 = \frac{3}{2} \cdot 7$

Cancel the common factor.

$\frac{1}{2} (2 c) + \frac{3}{2} \cdot - 12 = \frac{3}{2} \cdot 7$

Rewrite the expression.

$c + \frac{3}{2} \cdot - 12 = \frac{3}{2} \cdot 7$

Cancel the common factor of $2$ .

Factor $2$ out of $- 12$ .

$c + \frac{3}{2} \cdot (2 (- 6)) = \frac{3}{2} \cdot 7$

Cancel the common factor.

$c + \frac{3}{2} \cdot (2 \cdot - 6) = \frac{3}{2} \cdot 7$

Rewrite the expression.

$c + 3 \cdot - 6 = \frac{3}{2} \cdot 7$

Multiply $3$ by $- 6$ .

$c - 18 = \frac{3}{2} \cdot 7$

Simplify the right side.

Multiply $\frac{3}{2} \cdot 7$ .

Combine $\frac{3}{2}$ and $7$ .

$c - 18 = \frac{3 \cdot 7}{2}$

Multiply $3$ by $7$ .

$c - 18 = \frac{21}{2}$

Step 3

Move all terms not containing $c$ to the right side of the equation.

Add $18$ to both sides of the equation.

$c = \frac{21}{2} + 18$

To write $18$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$c = \frac{21}{2} + 18 \cdot \frac{2}{2}$

Combine $18$ and $\frac{2}{2}$ .

$c = \frac{21}{2} + \frac{18 \cdot 2}{2}$

Combine the numerators over the common denominator.

$c = \frac{21 + 18 \cdot 2}{2}$

Simplify the numerator.

Multiply $18$ by $2$ .

$c = \frac{21 + 36}{2}$

Add $21$ and $36$ .

$c = \frac{57}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$c = \frac{57}{2}$

Decimal Form:

$c = 28.5$

Mixed Number Form:

$c = 28 \frac{1}{2}$

Solve for c 2/3*(c-18)=7

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