Solve for u |4u+7|=5

$| 4 u + 7 | = 5$

Step 1

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

$4 u + 7 = \pm 5$

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.

$4 u + 7 = 5$

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

Subtract $7$ from both sides of the equation.

$4 u = 5 - 7$

Subtract $7$ from $5$ .

$4 u = - 2$

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $u$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $- 2$ and $4$ .

Factor $2$ out of $- 2$ .

$u = \frac{2 (- 1)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$u = \frac{2 \cdot - 1}{2 \cdot 2}$

Cancel the common factor.

$u = \frac{2 \cdot - 1}{2 \cdot 2}$

Rewrite the expression.

$u = \frac{- 1}{2}$

Move the negative in front of the fraction.

$u = - \frac{1}{2}$

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

$4 u + 7 = - 5$

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

Subtract $7$ from both sides of the equation.

$4 u = - 5 - 7$

Subtract $7$ from $- 5$ .

$4 u = - 12$

Divide each term in $4 u = - 12$ by $4$ and simplify.

Divide each term in $4 u = - 12$ by $4$ .

$\frac{4 u}{4} = \frac{- 12}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 u}{4} = \frac{- 12}{4}$

Divide $u$ by $1$ .

$u = \frac{- 12}{4}$

Simplify the right side.

Divide $- 12$ by $4$ .

$u = - 3$

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

$u = - \frac{1}{2}, - 3$

Step 3

The result can be shown in multiple forms.

Exact Form:

$u = - \frac{1}{2}, - 3$

Decimal Form:

$u = - 0.5, - 3$

Solve for u |4u+7|=5

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