Pre-Algebra Examples

$- 7 x + 4 \leq 32$

Step 1

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

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Step 1.1

Subtract $4$ from both sides of the inequality.

$- 7 x \leq 32 - 4$

Step 1.2

Subtract $4$ from $32$ .

$- 7 x \leq 28$

Step 2

Divide each term in $- 7 x \leq 28$ by $- 7$ and simplify.

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Step 2.1

Divide each term in $- 7 x \leq 28$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 x}{- 7} \geq \frac{28}{- 7}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 7$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 7 x}{- 7} \geq \frac{28}{- 7}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{28}{- 7}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $28$ by $- 7$ .

$x \geq - 4$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 4$

Interval Notation:

$[- 4, \infty)$