Basic Math Examples

$| 4 p - 7 | = | 3 p + 21 |$

Step 1

Rewrite the equation as $| 3 p + 21 | = | 4 p - 7 |$ .

$| 3 p + 21 | = | 4 p - 7 |$

Step 2

Rewrite the absolute value equation as four equations without absolute value bars.

$3 p + 21 = 4 p - 7$

$3 p + 21 = - (4 p - 7)$

$- (3 p + 21) = 4 p - 7$

$- (3 p + 21) = - (4 p - 7)$

Step 3

After simplifying, there are only two unique equations to be solved.

$3 p + 21 = 4 p - 7$

$3 p + 21 = - (4 p - 7)$

Step 4

Solve $3 p + 21 = 4 p - 7$ for $p$ .

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Subtract $4 p$ from both sides of the equation.

$3 p + 21 - 4 p = - 7$

Step 4.1.2

Subtract $4 p$ from $3 p$ .

$- p + 21 = - 7$

Step 4.2

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

Tap for more steps...

Step 4.2.1

Subtract $21$ from both sides of the equation.

$- p = - 7 - 21$

Step 4.2.2

Subtract $21$ from $- 7$ .

$- p = - 28$

Step 4.3

Divide each term in $- p = - 28$ by $- 1$ and simplify.

Tap for more steps...

Step 4.3.1

Divide each term in $- p = - 28$ by $- 1$ .

$\frac{- p}{- 1} = \frac{- 28}{- 1}$

Step 4.3.2

Simplify the left side.

Tap for more steps...

Step 4.3.2.1

Dividing two negative values results in a positive value.

$\frac{p}{1} = \frac{- 28}{- 1}$

Step 4.3.2.2

Divide $p$ by $1$ .

$p = \frac{- 28}{- 1}$

Step 4.3.3

Simplify the right side.

Tap for more steps...

Step 4.3.3.1

Divide $- 28$ by $- 1$ .

$p = 28$

Step 5

Solve $3 p + 21 = - (4 p - 7)$ for $p$ .

Tap for more steps...

Step 5.1

Simplify $- (4 p - 7)$ .

Tap for more steps...

Step 5.1.1

Rewrite.

$3 p + 21 = 0 + 0 - (4 p - 7)$

Step 5.1.2

Simplify by adding zeros.

$3 p + 21 = - (4 p - 7)$

Step 5.1.3

Apply the distributive property.

$3 p + 21 = - (4 p) - - 7$

Step 5.1.4

Multiply.

Tap for more steps...

Step 5.1.4.1

Multiply $4$ by $- 1$ .

$3 p + 21 = - 4 p - - 7$

Step 5.1.4.2

Multiply $- 1$ by $- 7$ .

$3 p + 21 = - 4 p + 7$

Step 5.2

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

Tap for more steps...

Step 5.2.1

Add $4 p$ to both sides of the equation.

$3 p + 21 + 4 p = 7$

Step 5.2.2

Add $3 p$ and $4 p$ .

$7 p + 21 = 7$

Step 5.3

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

Tap for more steps...

Step 5.3.1

Subtract $21$ from both sides of the equation.

$7 p = 7 - 21$

Step 5.3.2

Subtract $21$ from $7$ .

$7 p = - 14$

Step 5.4

Divide each term in $7 p = - 14$ by $7$ and simplify.

Tap for more steps...

Step 5.4.1

Divide each term in $7 p = - 14$ by $7$ .

$\frac{7 p}{7} = \frac{- 14}{7}$

Step 5.4.2

Simplify the left side.

Tap for more steps...

Step 5.4.2.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 5.4.2.1.1

Cancel the common factor.

$\frac{7 p}{7} = \frac{- 14}{7}$

Step 5.4.2.1.2

Divide $p$ by $1$ .

$p = \frac{- 14}{7}$

Step 5.4.3

Simplify the right side.

Tap for more steps...

Step 5.4.3.1

Divide $- 14$ by $7$ .

$p = - 2$

Step 6

List all of the solutions.

$p = 28, - 2$