Algebra Examples

$- 30 \leq - \frac{3}{4} (x + 4)$

Step 1

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

$- \frac{3}{4} \cdot (x + 4) \geq - 30$

Step 2

Multiply each term in $- \frac{3}{4} \cdot (x + 4) \geq - 30$ by $- \frac{4}{3}$ to eliminate the fractions.

Tap for more steps...

Step 2.1

Multiply each term in $- \frac{3}{4} \cdot (x + 4) \geq - 30$ by $- \frac{4}{3}$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$- \frac{3}{4} \cdot (x + 4) (- \frac{4}{3}) \leq - 30 (- \frac{4}{3})$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify terms.

Tap for more steps...

Step 2.2.1.1

Apply the distributive property.

$(- \frac{3}{4} x - \frac{3}{4} \cdot 4) (- \frac{4}{3}) \leq - 30 (- \frac{4}{3})$

Step 2.2.1.2

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

$(- \frac{x \cdot 3}{4} - \frac{3}{4} \cdot 4) (- \frac{4}{3}) \leq - 30 (- \frac{4}{3})$

Step 2.2.1.3

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.2.1.3.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$(- \frac{x \cdot 3}{4} + \frac{- 3}{4} \cdot 4) (- \frac{4}{3}) \leq - 30 (- \frac{4}{3})$

Step 2.2.1.3.2

Cancel the common factor.

$(- \frac{x \cdot 3}{4} + \frac{- 3}{4} \cdot 4) (- \frac{4}{3}) \leq - 30 (- \frac{4}{3})$

Step 2.2.1.3.3

Rewrite the expression.

$(- \frac{x \cdot 3}{4} - 3) (- \frac{4}{3}) \leq - 30 (- \frac{4}{3})$

Step 2.2.2

Move $3$ to the left of $x$ .

$(- \frac{3 x}{4} - 3) (- \frac{4}{3}) \leq - 30 (- \frac{4}{3})$

Step 2.2.3

Simplify terms.

Tap for more steps...

Step 2.2.3.1

Apply the distributive property.

$- \frac{3 x}{4} (- \frac{4}{3}) - 3 (- \frac{4}{3}) \leq - 30 (- \frac{4}{3})$

Step 2.2.3.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.3.2.1

Move the leading negative in $- \frac{3 x}{4}$ into the numerator.

$\frac{- 3 x}{4} (- \frac{4}{3}) - 3 (- \frac{4}{3}) \leq - 30 (- \frac{4}{3})$

Step 2.2.3.2.2

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$\frac{- 3 x}{4} \cdot \frac{- 4}{3} - 3 (- \frac{4}{3}) \leq - 30 (- \frac{4}{3})$

Step 2.2.3.2.3

Factor $3$ out of $- 3 x$ .

$\frac{3 (- x)}{4} \cdot \frac{- 4}{3} - 3 (- \frac{4}{3}) \leq - 30 (- \frac{4}{3})$

Step 2.2.3.2.4

Cancel the common factor.

$\frac{3 (- x)}{4} \cdot \frac{- 4}{3} - 3 (- \frac{4}{3}) \leq - 30 (- \frac{4}{3})$

Step 2.2.3.2.5

Rewrite the expression.

$\frac{- x}{4} \cdot - 4 - 3 (- \frac{4}{3}) \leq - 30 (- \frac{4}{3})$

Step 2.2.3.3

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.2.3.3.1

Factor $4$ out of $- 4$ .

$\frac{- x}{4} \cdot (4 (- 1)) - 3 (- \frac{4}{3}) \leq - 30 (- \frac{4}{3})$

Step 2.2.3.3.2

Cancel the common factor.

$\frac{- x}{4} \cdot (4 \cdot - 1) - 3 (- \frac{4}{3}) \leq - 30 (- \frac{4}{3})$

Step 2.2.3.3.3

Rewrite the expression.

$- x \cdot - 1 - 3 (- \frac{4}{3}) \leq - 30 (- \frac{4}{3})$

Step 2.2.3.4

Multiply.

Tap for more steps...

Step 2.2.3.4.1

Multiply $- 1$ by $- 1$ .

$1 x - 3 (- \frac{4}{3}) \leq - 30 (- \frac{4}{3})$

Step 2.2.3.4.2

Multiply $x$ by $1$ .

$x - 3 (- \frac{4}{3}) \leq - 30 (- \frac{4}{3})$

Step 2.2.3.5

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.3.5.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$x - 3 (\frac{- 4}{3}) \leq - 30 (- \frac{4}{3})$

Step 2.2.3.5.2

Factor $3$ out of $- 3$ .

$x + 3 (- 1) \frac{- 4}{3} \leq - 30 (- \frac{4}{3})$

Step 2.2.3.5.3

Cancel the common factor.

$x + 3 \cdot - 1 \frac{- 4}{3} \leq - 30 (- \frac{4}{3})$

Step 2.2.3.5.4

Rewrite the expression.

$x - 1 \cdot - 4 \leq - 30 (- \frac{4}{3})$

Step 2.2.3.6

Multiply $- 1$ by $- 4$ .

$x + 4 \leq - 30 (- \frac{4}{3})$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.3.1.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$x + 4 \leq - 30 (\frac{- 4}{3})$

Step 2.3.1.2

Factor $3$ out of $- 30$ .

$x + 4 \leq 3 (- 10) \frac{- 4}{3}$

Step 2.3.1.3

Cancel the common factor.

$x + 4 \leq 3 \cdot - 10 \frac{- 4}{3}$

Step 2.3.1.4

Rewrite the expression.

$x + 4 \leq - 10 \cdot - 4$

Step 2.3.2

Multiply $- 10$ by $- 4$ .

$x + 4 \leq 40$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $4$ from both sides of the inequality.

$x \leq 40 - 4$

Step 3.2

Subtract $4$ from $40$ .

$x \leq 36$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq 36$

Interval Notation:

$(- \infty, 36]$