Algebra Examples

$\frac{3}{4} x = 7 - x$

Step 1

Simplify $\frac{3}{4} x$ .

Tap for more steps...

Step 1.1

Rewrite.

$0 + 0 + \frac{3}{4} x = 7 - x$

Step 1.2

Simplify by adding zeros.

$\frac{3}{4} x = 7 - x$

Step 1.3

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

$\frac{3 x}{4} = 7 - x$

Step 2

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

Tap for more steps...

Step 2.1

Add $x$ to both sides of the equation.

$\frac{3 x}{4} + x = 7$

Step 2.2

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

$\frac{3 x}{4} + x \cdot \frac{4}{4} = 7$

Step 2.3

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

$\frac{3 x}{4} + \frac{x \cdot 4}{4} = 7$

Step 2.4

Combine the numerators over the common denominator.

$\frac{3 x + x \cdot 4}{4} = 7$

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Move $4$ to the left of $x$ .

$\frac{3 x + 4 \cdot x}{4} = 7$

Step 2.5.2

Add $3 x$ and $4 x$ .

$\frac{7 x}{4} = 7$

Step 3

Multiply both sides of the equation by $\frac{4}{7}$ .

$\frac{4}{7} \cdot \frac{7 x}{4} = \frac{4}{7} \cdot 7$

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 $\frac{4}{7} \cdot \frac{7 x}{4}$ .

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.

$\frac{4}{7} \cdot \frac{7 x}{4} = \frac{4}{7} \cdot 7$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{4}{7} \cdot 7$

Step 4.1.1.2

Cancel the common factor of $7$ .

Tap for more steps...

Step 4.1.1.2.1

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{4}{7} \cdot 7$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{4}{7} \cdot 7$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{4}{7} \cdot 7$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$x = \frac{4}{7} \cdot 7$

Step 4.2.1.2

Rewrite the expression.

$x = 4$