Algebra Examples

$- 9 \geq \frac{2}{5} x + 7$

Step 1

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

$\frac{2}{5} x + 7 \leq - 9$

Step 2

Combine $\frac{2}{5}$ and $x$ .

$\frac{2 x}{5} + 7 \leq - 9$

Step 3

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

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Step 3.1

Subtract $7$ from both sides of the inequality.

$\frac{2 x}{5} \leq - 9 - 7$

Step 3.2

Subtract $7$ from $- 9$ .

$\frac{2 x}{5} \leq - 16$

Step 4

Multiply both sides by $5$ .

$\frac{2 x}{5} \cdot 5 \leq - 16 \cdot 5$

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 $5$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{2 x}{5} \cdot 5 \leq - 16 \cdot 5$

Step 5.1.1.2

Rewrite the expression.

$2 x \leq - 16 \cdot 5$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 16$ by $5$ .

$2 x \leq - 80$

Step 6

Divide each term in $2 x \leq - 80$ by $2$ and simplify.

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Step 6.1

Divide each term in $2 x \leq - 80$ by $2$ .

$\frac{2 x}{2} \leq \frac{- 80}{2}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $2$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{- 80}{2}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{- 80}{2}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $- 80$ by $2$ .

$x \leq - 40$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 40$

Interval Notation:

$(- \infty, - 40]$