Algebra Examples

$\frac{3}{4} > - (x - 3) + 2 x$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$- (x - 3) + 2 x < \frac{3}{4}$

Step 2

Simplify $- (x - 3) + 2 x$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Apply the distributive property.

$- x - - 3 + 2 x < \frac{3}{4}$

Step 2.1.2

Multiply $- 1$ by $- 3$ .

$- x + 3 + 2 x < \frac{3}{4}$

Step 2.2

Add $- x$ and $2 x$ .

$x + 3 < \frac{3}{4}$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $3$ from both sides of the inequality.

$x < \frac{3}{4} - 3$

Step 3.2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x < \frac{3}{4} - 3 \cdot \frac{4}{4}$

Step 3.3

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

$x < \frac{3}{4} + \frac{- 3 \cdot 4}{4}$

Step 3.4

Combine the numerators over the common denominator.

$x < \frac{3 - 3 \cdot 4}{4}$

Step 3.5

Simplify the numerator.

Tap for more steps...

Step 3.5.1

Multiply $- 3$ by $4$ .

$x < \frac{3 - 12}{4}$

Step 3.5.2

Subtract $12$ from $3$ .

$x < \frac{- 9}{4}$

Step 3.6

Move the negative in front of the fraction.

$x < - \frac{9}{4}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < - \frac{9}{4}$

Interval Notation:

$(- \infty, - \frac{9}{4})$