Algebra Examples

$x - 42 + \frac{1}{4} x + 21 + 2 x - 59 = 180$

Step 1

Simplify $x - 42 + \frac{1}{4} x + 21 + 2 x - 59$ .

Tap for more steps...

Step 1.1

Combine $\frac{1}{4}$ and $x$ .

$x - 42 + \frac{x}{4} + 21 + 2 x - 59 = 180$

Step 1.2

To write $x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x \cdot \frac{4}{4} + \frac{x}{4} - 42 + 21 + 2 x - 59 = 180$

Step 1.3

Combine $x$ and $\frac{4}{4}$ .

$\frac{x \cdot 4}{4} + \frac{x}{4} - 42 + 21 + 2 x - 59 = 180$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 4 + x}{4} - 42 + 21 + 2 x - 59 = 180$

Step 1.5

Add $x \cdot 4$ and $x$ .

Tap for more steps...

Step 1.5.1

Reorder $x$ and $4$ .

$\frac{4 \cdot x + x}{4} - 42 + 21 + 2 x - 59 = 180$

Step 1.5.2

Add $4 \cdot x$ and $x$ .

$\frac{5 \cdot x}{4} - 42 + 21 + 2 x - 59 = 180$

Step 1.6

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5 x}{4} + 2 x \cdot \frac{4}{4} - 42 + 21 - 59 = 180$

Step 1.7

Combine $2 x$ and $\frac{4}{4}$ .

$\frac{5 x}{4} + \frac{2 x \cdot 4}{4} - 42 + 21 - 59 = 180$

Step 1.8

Combine the numerators over the common denominator.

$\frac{5 x + 2 x \cdot 4}{4} - 42 + 21 - 59 = 180$

Step 1.9

Find the common denominator.

Tap for more steps...

Step 1.9.1

Write $- 42$ as a fraction with denominator $1$ .

$\frac{5 x + 2 x \cdot 4}{4} + \frac{- 42}{1} + 21 - 59 = 180$

Step 1.9.2

Multiply $\frac{- 42}{1}$ by $\frac{4}{4}$ .

$\frac{5 x + 2 x \cdot 4}{4} + \frac{- 42}{1} \cdot \frac{4}{4} + 21 - 59 = 180$

Step 1.9.3

Multiply $\frac{- 42}{1}$ by $\frac{4}{4}$ .

$\frac{5 x + 2 x \cdot 4}{4} + \frac{- 42 \cdot 4}{4} + 21 - 59 = 180$

Step 1.9.4

Write $21$ as a fraction with denominator $1$ .

$\frac{5 x + 2 x \cdot 4}{4} + \frac{- 42 \cdot 4}{4} + \frac{21}{1} - 59 = 180$

Step 1.9.5

Multiply $\frac{21}{1}$ by $\frac{4}{4}$ .

$\frac{5 x + 2 x \cdot 4}{4} + \frac{- 42 \cdot 4}{4} + \frac{21}{1} \cdot \frac{4}{4} - 59 = 180$

Step 1.9.6

Multiply $\frac{21}{1}$ by $\frac{4}{4}$ .

$\frac{5 x + 2 x \cdot 4}{4} + \frac{- 42 \cdot 4}{4} + \frac{21 \cdot 4}{4} - 59 = 180$

Step 1.9.7

Write $- 59$ as a fraction with denominator $1$ .

$\frac{5 x + 2 x \cdot 4}{4} + \frac{- 42 \cdot 4}{4} + \frac{21 \cdot 4}{4} + \frac{- 59}{1} = 180$

Step 1.9.8

Multiply $\frac{- 59}{1}$ by $\frac{4}{4}$ .

$\frac{5 x + 2 x \cdot 4}{4} + \frac{- 42 \cdot 4}{4} + \frac{21 \cdot 4}{4} + \frac{- 59}{1} \cdot \frac{4}{4} = 180$

Step 1.9.9

Multiply $\frac{- 59}{1}$ by $\frac{4}{4}$ .

$\frac{5 x + 2 x \cdot 4}{4} + \frac{- 42 \cdot 4}{4} + \frac{21 \cdot 4}{4} + \frac{- 59 \cdot 4}{4} = 180$

Step 1.10

Combine the numerators over the common denominator.

$\frac{5 x + 2 x \cdot 4 - 42 \cdot 4 + 21 \cdot 4 - 59 \cdot 4}{4} = 180$

Step 1.11

Simplify each term.

Tap for more steps...

Step 1.11.1

Multiply $4$ by $2$ .

$\frac{5 x + 8 x - 42 \cdot 4 + 21 \cdot 4 - 59 \cdot 4}{4} = 180$

Step 1.11.2

Multiply $- 42$ by $4$ .

$\frac{5 x + 8 x - 168 + 21 \cdot 4 - 59 \cdot 4}{4} = 180$

Step 1.11.3

Multiply $21$ by $4$ .

$\frac{5 x + 8 x - 168 + 84 - 59 \cdot 4}{4} = 180$

Step 1.11.4

Multiply $- 59$ by $4$ .

$\frac{5 x + 8 x - 168 + 84 - 236}{4} = 180$

Step 1.12

Simplify by adding terms.

Tap for more steps...

Step 1.12.1

Add $5 x$ and $8 x$ .

$\frac{13 x - 168 + 84 - 236}{4} = 180$

Step 1.12.2

Simplify by adding and subtracting.

Tap for more steps...

Step 1.12.2.1

Add $- 168$ and $84$ .

$\frac{13 x - 84 - 236}{4} = 180$

Step 1.12.2.2

Subtract $236$ from $- 84$ .

$\frac{13 x - 320}{4} = 180$

Step 2

Multiply both sides by $4$ .

$\frac{13 x - 320}{4} \cdot 4 = 180 \cdot 4$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor.

$\frac{13 x - 320}{4} \cdot 4 = 180 \cdot 4$

Step 3.1.1.2

Rewrite the expression.

$13 x - 320 = 180 \cdot 4$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Multiply $180$ by $4$ .

$13 x - 320 = 720$

Step 4

Solve for $x$ .

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Add $320$ to both sides of the equation.

$13 x = 720 + 320$

Step 4.1.2

Add $720$ and $320$ .

$13 x = 1040$

Step 4.2

Divide each term in $13 x = 1040$ by $13$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $13 x = 1040$ by $13$ .

$\frac{13 x}{13} = \frac{1040}{13}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $13$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{13 x}{13} = \frac{1040}{13}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1040}{13}$

Step 4.2.3

Simplify the right side.

Tap for more steps...

Step 4.2.3.1

Divide $1040$ by $13$ .

$x = 80$