Pre-Algebra Examples

$\frac{6 - x}{5} + \frac{x}{10} = \frac{3}{2}$

Step 1

Simplify $\frac{6 - x}{5} + \frac{x}{10}$ .

Tap for more steps...

Step 1.1

To write $\frac{6 - x}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{6 - x}{5} \cdot \frac{2}{2} + \frac{x}{10} = \frac{3}{2}$

Step 1.2

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.2.1

Multiply $\frac{6 - x}{5}$ by $\frac{2}{2}$ .

$\frac{(6 - x) \cdot 2}{5 \cdot 2} + \frac{x}{10} = \frac{3}{2}$

Step 1.2.2

Multiply $5$ by $2$ .

$\frac{(6 - x) \cdot 2}{10} + \frac{x}{10} = \frac{3}{2}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{(6 - x) \cdot 2 + x}{10} = \frac{3}{2}$

Step 1.4

Simplify the numerator.

Tap for more steps...

Step 1.4.1

Apply the distributive property.

$\frac{6 \cdot 2 - x \cdot 2 + x}{10} = \frac{3}{2}$

Step 1.4.2

Multiply $6$ by $2$ .

$\frac{12 - x \cdot 2 + x}{10} = \frac{3}{2}$

Step 1.4.3

Multiply $2$ by $- 1$ .

$\frac{12 - 2 x + x}{10} = \frac{3}{2}$

Step 1.4.4

Add $- 2 x$ and $x$ .

$\frac{12 - x}{10} = \frac{3}{2}$

Step 2

Multiply both sides by $10$ .

$\frac{12 - x}{10} \cdot 10 = \frac{3}{2} \cdot 10$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $\frac{12 - x}{10} \cdot 10$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor of $10$ .

Tap for more steps...

Step 3.1.1.1.1

Cancel the common factor.

$\frac{12 - x}{10} \cdot 10 = \frac{3}{2} \cdot 10$

Step 3.1.1.1.2

Rewrite the expression.

$12 - x = \frac{3}{2} \cdot 10$

Step 3.1.1.2

Reorder $12$ and $- x$ .

$- x + 12 = \frac{3}{2} \cdot 10$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Simplify $\frac{3}{2} \cdot 10$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.1.1

Factor $2$ out of $10$ .

$- x + 12 = \frac{3}{2} \cdot (2 (5))$

Step 3.2.1.1.2

Cancel the common factor.

$- x + 12 = \frac{3}{2} \cdot (2 \cdot 5)$

Step 3.2.1.1.3

Rewrite the expression.

$- x + 12 = 3 \cdot 5$

Step 3.2.1.2

Multiply $3$ by $5$ .

$- x + 12 = 15$

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

Subtract $12$ from both sides of the equation.

$- x = 15 - 12$

Step 4.1.2

Subtract $12$ from $15$ .

$- x = 3$

Step 4.2

Divide each term in $- x = 3$ by $- 1$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $- x = 3$ by $- 1$ .

$\frac{- x}{- 1} = \frac{3}{- 1}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{3}{- 1}$

Step 4.2.2.2

Divide $x$ by $1$ .

$x = \frac{3}{- 1}$

Step 4.2.3

Simplify the right side.

Tap for more steps...

Step 4.2.3.1

Divide $3$ by $- 1$ .

$x = - 3$