Solve for p 10=43-|7p+12|

$10 = 43 - | 7 p + 12 |$

Step 1

Rewrite the equation as $43 - | 7 p + 12 | = 10$ .

$43 - | 7 p + 12 | = 10$

Step 2

Move all terms not containing $| 7 p + 12 |$ to the right side of the equation.

Subtract $43$ from both sides of the equation.

$- | 7 p + 12 | = 10 - 43$

Subtract $43$ from $10$ .

$- | 7 p + 12 | = - 33$

Step 3

Divide each term in $- | 7 p + 12 | = - 33$ by $- 1$ and simplify.

Divide each term in $- | 7 p + 12 | = - 33$ by $- 1$ .

$\frac{- | 7 p + 12 |}{- 1} = \frac{- 33}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{| 7 p + 12 |}{1} = \frac{- 33}{- 1}$

Divide $| 7 p + 12 |$ by $1$ .

$| 7 p + 12 | = \frac{- 33}{- 1}$

Simplify the right side.

Divide $- 33$ by $- 1$ .

$| 7 p + 12 | = 33$

Step 4

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

$7 p + 12 = \pm 33$

Step 5

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.

$7 p + 12 = 33$

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

Subtract $12$ from both sides of the equation.

$7 p = 33 - 12$

Subtract $12$ from $33$ .

$7 p = 21$

Divide each term in $7 p = 21$ by $7$ and simplify.

Divide each term in $7 p = 21$ by $7$ .

$\frac{7 p}{7} = \frac{21}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 p}{7} = \frac{21}{7}$

Divide $p$ by $1$ .

$p = \frac{21}{7}$

Simplify the right side.

Divide $21$ by $7$ .

$p = 3$

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

$7 p + 12 = - 33$

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

Subtract $12$ from both sides of the equation.

$7 p = - 33 - 12$

Subtract $12$ from $- 33$ .

$7 p = - 45$

Divide each term in $7 p = - 45$ by $7$ and simplify.

Divide each term in $7 p = - 45$ by $7$ .

$\frac{7 p}{7} = \frac{- 45}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 p}{7} = \frac{- 45}{7}$

Divide $p$ by $1$ .

$p = \frac{- 45}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$p = - \frac{45}{7}$

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

$p = 3, - \frac{45}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$p = 3, - \frac{45}{7}$

Decimal Form:

$p = 3, - 6.\overline{428571}$

Mixed Number Form:

$p = 3, - 6 \frac{3}{7}$

Solve for p 10=43-|7p+12|

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