Solve for x -3|1+4x|-4=-7

$- 3 | 1 + 4 x | - 4 = - 7$

Step 1

Move all terms not containing $| 1 + 4 x |$ to the right side of the equation.

Add $4$ to both sides of the equation.

$- 3 | 1 + 4 x | = - 7 + 4$

Add $- 7$ and $4$ .

$- 3 | 1 + 4 x | = - 3$

Step 2

Divide each term in $- 3 | 1 + 4 x | = - 3$ by $- 3$ and simplify.

Divide each term in $- 3 | 1 + 4 x | = - 3$ by $- 3$ .

$\frac{- 3 | 1 + 4 x |}{- 3} = \frac{- 3}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 | 1 + 4 x |}{- 3} = \frac{- 3}{- 3}$

Divide $| 1 + 4 x |$ by $1$ .

$| 1 + 4 x | = \frac{- 3}{- 3}$

Simplify the right side.

Divide $- 3$ by $- 3$ .

$| 1 + 4 x | = 1$

Step 3

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

$1 + 4 x = \pm 1$

Step 4

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.

$1 + 4 x = 1$

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

Subtract $1$ from both sides of the equation.

$4 x = 1 - 1$

Subtract $1$ from $1$ .

$4 x = 0$

Divide each term in $4 x = 0$ by $4$ and simplify.

Divide each term in $4 x = 0$ by $4$ .

$\frac{4 x}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{0}{4}$

Divide $x$ by $1$ .

$x = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$x = 0$

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

$1 + 4 x = - 1$

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

Subtract $1$ from both sides of the equation.

$4 x = - 1 - 1$

Subtract $1$ from $- 1$ .

$4 x = - 2$

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

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

Factor $2$ out of $- 2$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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

$x = 0, - \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 0, - \frac{1}{2}$

Decimal Form:

$x = 0, - 0.5$

Solve for x -3|1+4x|-4=-7

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