Solve for c |7-2c|=3

$| 7 - 2 c | = 3$

Step 1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$7 - 2 c = \pm 3$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$7 - 2 c = 3$

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

Subtract $7$ from both sides of the equation.

$- 2 c = 3 - 7$

Subtract $7$ from $3$ .

$- 2 c = - 4$

Divide each term in $- 2 c = - 4$ by $- 2$ and simplify.

Divide each term in $- 2 c = - 4$ by $- 2$ .

$\frac{- 2 c}{- 2} = \frac{- 4}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 c}{- 2} = \frac{- 4}{- 2}$

Divide $c$ by $1$ .

$c = \frac{- 4}{- 2}$

Simplify the right side.

Divide $- 4$ by $- 2$ .

$c = 2$

Next, use the negative value of the $\pm$ to find the second solution.

$7 - 2 c = - 3$

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

Subtract $7$ from both sides of the equation.

$- 2 c = - 3 - 7$

Subtract $7$ from $- 3$ .

$- 2 c = - 10$

Divide each term in $- 2 c = - 10$ by $- 2$ and simplify.

Divide each term in $- 2 c = - 10$ by $- 2$ .

$\frac{- 2 c}{- 2} = \frac{- 10}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 c}{- 2} = \frac{- 10}{- 2}$

Divide $c$ by $1$ .

$c = \frac{- 10}{- 2}$

Simplify the right side.

Divide $- 10$ by $- 2$ .

$c = 5$

The complete solution is the result of both the positive and negative portions of the solution.

$c = 2, 5$

Solve for c |7-2c|=3

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