Solve for x |4x+3|+9=2x

$| 4 x + 3 | + 9 = 2 x$

Step 1

Subtract $9$ from both sides of the equation.

$| 4 x + 3 | = 2 x - 9$

Step 2

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

$4 x + 3 = \pm (2 x - 9)$

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.

$4 x + 3 = 2 x - 9$

Move all terms containing $x$ to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

$4 x + 3 - 2 x = - 9$

Subtract $2 x$ from $4 x$ .

$2 x + 3 = - 9$

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

Subtract $3$ from both sides of the equation.

$2 x = - 9 - 3$

Subtract $3$ from $- 9$ .

$2 x = - 12$

Divide each term in $2 x = - 12$ by $2$ and simplify.

Divide each term in $2 x = - 12$ by $2$ .

$\frac{2 x}{2} = \frac{- 12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 12}{2}$

Divide $x$ by $1$ .

$x = \frac{- 12}{2}$

Simplify the right side.

Divide $- 12$ by $2$ .

$x = - 6$

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

$4 x + 3 = - (2 x - 9)$

Simplify $- (2 x - 9)$ .

Rewrite.

$4 x + 3 = 0 + 0 - (2 x - 9)$

Simplify by adding zeros.

$4 x + 3 = - (2 x - 9)$

Apply the distributive property.

$4 x + 3 = - (2 x) - - 9$

Multiply.

Multiply $2$ by $- 1$ .

$4 x + 3 = - 2 x - - 9$

Multiply $- 1$ by $- 9$ .

$4 x + 3 = - 2 x + 9$

Move all terms containing $x$ to the left side of the equation.

Add $2 x$ to both sides of the equation.

$4 x + 3 + 2 x = 9$

Add $4 x$ and $2 x$ .

$6 x + 3 = 9$

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

Subtract $3$ from both sides of the equation.

$6 x = 9 - 3$

Subtract $3$ from $9$ .

$6 x = 6$

Divide each term in $6 x = 6$ by $6$ and simplify.

Divide each term in $6 x = 6$ by $6$ .

$\frac{6 x}{6} = \frac{6}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{6}{6}$

Divide $x$ by $1$ .

$x = \frac{6}{6}$

Simplify the right side.

Divide $6$ by $6$ .

$x = 1$

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

$x = - 6, 1$

Step 4

Exclude the solutions that do not make $| 4 x + 3 | + 9 = 2 x$ true.

$No solution$

Solve for x |4x+3|+9=2x

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