Algebra Examples

$\frac{1}{2} x + \frac{3}{4} x = 5 - 2.5 x$

Step 1

Simplify $\frac{1}{2} x + \frac{3}{4} x$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} + \frac{3}{4} x = 5 - 2.5 x$

Step 1.1.2

Combine $\frac{3}{4}$ and $x$ .

$\frac{x}{2} + \frac{3 x}{4} = 5 - 2.5 x$

Step 1.2

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

$\frac{x}{2} \cdot \frac{2}{2} + \frac{3 x}{4} = 5 - 2.5 x$

Step 1.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.3.1

Multiply $\frac{x}{2}$ by $\frac{2}{2}$ .

$\frac{x \cdot 2}{2 \cdot 2} + \frac{3 x}{4} = 5 - 2.5 x$

Step 1.3.2

Multiply $2$ by $2$ .

$\frac{x \cdot 2}{4} + \frac{3 x}{4} = 5 - 2.5 x$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + 3 x}{4} = 5 - 2.5 x$

Step 1.5

Simplify the numerator.

Tap for more steps...

Step 1.5.1

Move $2$ to the left of $x$ .

$\frac{2 \cdot x + 3 x}{4} = 5 - 2.5 x$

Step 1.5.2

Add $2 x$ and $3 x$ .

$\frac{5 x}{4} = 5 - 2.5 x$

Step 2

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

Tap for more steps...

Step 2.1

Add $2.5 x$ to both sides of the equation.

$\frac{5 x}{4} + 2.5 x = 5$

Step 2.2

To write $2.5 x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5 x}{4} + 2.5 x \cdot \frac{4}{4} = 5$

Step 2.3

Combine $2.5 x$ and $\frac{4}{4}$ .

$\frac{5 x}{4} + \frac{2.5 x \cdot 4}{4} = 5$

Step 2.4

Combine the numerators over the common denominator.

$\frac{5 x + 2.5 x \cdot 4}{4} = 5$

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Factor $2.5 x$ out of $5 x + 2.5 x \cdot 4$ .

Tap for more steps...

Step 2.5.1.1

Move $x$ .

$\frac{5 x + 2.5 \cdot 4 x}{4} = 5$

Step 2.5.1.2

Factor $2.5 x$ out of $5 x$ .

$\frac{2.5 x (2) + 2.5 \cdot 4 x}{4} = 5$

Step 2.5.1.3

Factor $2.5 x$ out of $2.5 \cdot 4 x$ .

$\frac{2.5 x (2) + 2.5 x (4)}{4} = 5$

Step 2.5.1.4

Factor $2.5 x$ out of $2.5 x (2) + 2.5 x (4)$ .

$\frac{2.5 x (2 + 4)}{4} = 5$

Step 2.5.2

Multiply $2 + 4$ by $2.5$ .

$\frac{15 x}{4} = 5$

Step 2.6

Cancel the common factor of $15$ and $4$ .

Tap for more steps...

Step 2.6.1

Factor $1$ out of $15 x$ .

$\frac{1 (15 x)}{4} = 5$

Step 2.6.2

Cancel the common factors.

Tap for more steps...

Step 2.6.2.1

Rewrite $4$ as $1 (4)$ .

$\frac{1 (15 x)}{1 (4)} = 5$

Step 2.6.2.2

Cancel the common factor.

$\frac{1 (15 x)}{1 \cdot 4} = 5$

Step 2.6.2.3

Rewrite the expression.

$\frac{15 x}{4} = 5$

Step 3

Multiply both sides of the equation by $\frac{4}{15}$ .

$\frac{4}{15} \cdot \frac{15 x}{4} = \frac{4}{15} \cdot 5$

Step 4

Simplify both sides of the equation.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

Simplify $\frac{4}{15} \cdot \frac{15 x}{4}$ .

Tap for more steps...

Step 4.1.1.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.1.1.1.1

Cancel the common factor.

$\frac{4}{15} \cdot \frac{15 x}{4} = \frac{4}{15} \cdot 5$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{15} (15 x) = \frac{4}{15} \cdot 5$

Step 4.1.1.2

Cancel the common factor of $15$ .

Tap for more steps...

Step 4.1.1.2.1

Factor $15$ out of $15 x$ .

$\frac{1}{15} (15 (x)) = \frac{4}{15} \cdot 5$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{15} (15 x) = \frac{4}{15} \cdot 5$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{4}{15} \cdot 5$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 4.2.1.1

Factor $5$ out of $15$ .

$x = \frac{4}{5 (3)} \cdot 5$

Step 4.2.1.2

Cancel the common factor.

$x = \frac{4}{5 \cdot 3} \cdot 5$

Step 4.2.1.3

Rewrite the expression.

$x = \frac{4}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{3}$

Decimal Form:

$x = 1.\overline{3}$

Mixed Number Form:

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