Pre-Algebra Examples

$\frac{x}{- 4} - 3 \geq - 23$

Step 1

Move the negative in front of the fraction.

$- \frac{x}{4} - 3 \geq - 23$

Step 2

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

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Step 2.1

Add $3$ to both sides of the inequality.

$- \frac{x}{4} \geq - 23 + 3$

Step 2.2

Add $- 23$ and $3$ .

$- \frac{x}{4} \geq - 20$

Step 3

Divide each term in $- \frac{x}{4} \geq - 20$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- \frac{x}{4} \geq - 20$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{x}{4}}{- 1} \leq \frac{- 20}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{x}{4}}{1} \leq \frac{- 20}{- 1}$

Step 3.2.2

Divide $\frac{x}{4}$ by $1$ .

$\frac{x}{4} \leq \frac{- 20}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 20$ by $- 1$ .

$\frac{x}{4} \leq 20$

Step 4

Multiply both sides by $4$ .

$\frac{x}{4} \cdot 4 \leq 20 \cdot 4$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{x}{4} \cdot 4 \leq 20 \cdot 4$

Step 5.1.1.2

Rewrite the expression.

$x \leq 20 \cdot 4$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $20$ by $4$ .

$x \leq 80$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x \leq 80$

Interval Notation:

$(- \infty, 80]$