Solve for x 4+|4x-7|=16

$4 + | 4 x - 7 | = 16$

Step 1

Move all terms not containing $| 4 x - 7 |$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$| 4 x - 7 | = 16 - 4$

Subtract $4$ from $16$ .

$| 4 x - 7 | = 12$

Step 2

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

$4 x - 7 = \pm 12$

Step 3

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.

$4 x - 7 = 12$

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

Add $7$ to both sides of the equation.

$4 x = 12 + 7$

Add $12$ and $7$ .

$4 x = 19$

Divide each term in $4 x = 19$ by $4$ and simplify.

Divide each term in $4 x = 19$ by $4$ .

$\frac{4 x}{4} = \frac{19}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{19}{4}$

Divide $x$ by $1$ .

$x = \frac{19}{4}$

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

$4 x - 7 = - 12$

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

Add $7$ to both sides of the equation.

$4 x = - 12 + 7$

Add $- 12$ and $7$ .

$4 x = - 5$

Divide each term in $4 x = - 5$ by $4$ and simplify.

Divide each term in $4 x = - 5$ by $4$ .

$\frac{4 x}{4} = \frac{- 5}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 5}{4}$

Divide $x$ by $1$ .

$x = \frac{- 5}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{5}{4}$

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

$x = \frac{19}{4}, - \frac{5}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{19}{4}, - \frac{5}{4}$

Decimal Form:

$x = 4.75, - 1.25$

Mixed Number Form:

$x = 4 \frac{3}{4}, - 1 \frac{1}{4}$

Solve for x 4+|4x-7|=16

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