Solve for p 9|4p+2|+8=35

$9 | 4 p + 2 | + 8 = 35$

Step 1

Move all terms not containing $| 4 p + 2 |$ to the right side of the equation.

Subtract $8$ from both sides of the equation.

$9 | 4 p + 2 | = 35 - 8$

Subtract $8$ from $35$ .

$9 | 4 p + 2 | = 27$

Step 2

Divide each term in $9 | 4 p + 2 | = 27$ by $9$ and simplify.

Divide each term in $9 | 4 p + 2 | = 27$ by $9$ .

$\frac{9 | 4 p + 2 |}{9} = \frac{27}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 | 4 p + 2 |}{9} = \frac{27}{9}$

Divide $| 4 p + 2 |$ by $1$ .

$| 4 p + 2 | = \frac{27}{9}$

Simplify the right side.

Divide $27$ by $9$ .

$| 4 p + 2 | = 3$

Step 3

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

$4 p + 2 = \pm 3$

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.

$4 p + 2 = 3$

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

Subtract $2$ from both sides of the equation.

$4 p = 3 - 2$

Subtract $2$ from $3$ .

$4 p = 1$

Divide each term in $4 p = 1$ by $4$ and simplify.

Divide each term in $4 p = 1$ by $4$ .

$\frac{4 p}{4} = \frac{1}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 p}{4} = \frac{1}{4}$

Divide $p$ by $1$ .

$p = \frac{1}{4}$

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

$4 p + 2 = - 3$

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

Subtract $2$ from both sides of the equation.

$4 p = - 3 - 2$

Subtract $2$ from $- 3$ .

$4 p = - 5$

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $p$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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

$p = \frac{1}{4}, - \frac{5}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$p = \frac{1}{4}, - \frac{5}{4}$

Decimal Form:

$p = 0.25, - 1.25$

Mixed Number Form:

$p = \frac{1}{4}, - 1 \frac{1}{4}$

Solve for p 9|4p+2|+8=35

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