Pre-Algebra Examples

$5 \cdot | 11 - 3 x | - 7 = 33$

Step 1

Move all terms not containing $| 11 - 3 x |$ to the right side of the equation.

Tap for more steps...

Step 1.1

Add $7$ to both sides of the equation.

$5 | 11 - 3 x | = 33 + 7$

Step 1.2

Add $33$ and $7$ .

$5 | 11 - 3 x | = 40$

Step 2

Divide each term in $5 | 11 - 3 x | = 40$ by $5$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $5 | 11 - 3 x | = 40$ by $5$ .

$\frac{5 | 11 - 3 x |}{5} = \frac{40}{5}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{5 | 11 - 3 x |}{5} = \frac{40}{5}$

Step 2.2.1.2

Divide $| 11 - 3 x |$ by $1$ .

$| 11 - 3 x | = \frac{40}{5}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Divide $40$ by $5$ .

$| 11 - 3 x | = 8$

Step 3

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

$11 - 3 x = \pm 8$

Step 4

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

Tap for more steps...

Step 4.1

First, use the positive value of the $\pm$ to find the first solution.

$11 - 3 x = 8$

Step 4.2

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

Tap for more steps...

Step 4.2.1

Subtract $11$ from both sides of the equation.

$- 3 x = 8 - 11$

Step 4.2.2

Subtract $11$ from $8$ .

$- 3 x = - 3$

Step 4.3

Divide each term in $- 3 x = - 3$ by $- 3$ and simplify.

Tap for more steps...

Step 4.3.1

Divide each term in $- 3 x = - 3$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 3}{- 3}$

Step 4.3.2

Simplify the left side.

Tap for more steps...

Step 4.3.2.1

Cancel the common factor of $- 3$ .

Tap for more steps...

Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 3}{- 3}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 3}{- 3}$

Step 4.3.3

Simplify the right side.

Tap for more steps...

Step 4.3.3.1

Divide $- 3$ by $- 3$ .

$x = 1$

Step 4.4

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

$11 - 3 x = - 8$

Step 4.5

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

Tap for more steps...

Step 4.5.1

Subtract $11$ from both sides of the equation.

$- 3 x = - 8 - 11$

Step 4.5.2

Subtract $11$ from $- 8$ .

$- 3 x = - 19$

Step 4.6

Divide each term in $- 3 x = - 19$ by $- 3$ and simplify.

Tap for more steps...

Step 4.6.1

Divide each term in $- 3 x = - 19$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 19}{- 3}$

Step 4.6.2

Simplify the left side.

Tap for more steps...

Step 4.6.2.1

Cancel the common factor of $- 3$ .

Tap for more steps...

Step 4.6.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 19}{- 3}$

Step 4.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 19}{- 3}$

Step 4.6.3

Simplify the right side.

Tap for more steps...

Step 4.6.3.1

Dividing two negative values results in a positive value.

$x = \frac{19}{3}$

Step 4.7

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

$x = 1, \frac{19}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 1, \frac{19}{3}$

Decimal Form:

$x = 1, 6.\overline{3}$

Mixed Number Form:

$x = 1, 6 \frac{1}{3}$