Pre-Algebra Examples

$\frac{4}{5} x + 5 < - 3$

Step 1

Combine $\frac{4}{5}$ and $x$ .

$\frac{4 x}{5} + 5 < - 3$

Step 2

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

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Step 2.1

Subtract $5$ from both sides of the inequality.

$\frac{4 x}{5} < - 3 - 5$

Step 2.2

Subtract $5$ from $- 3$ .

$\frac{4 x}{5} < - 8$

Step 3

Multiply both sides by $5$ .

$\frac{4 x}{5} \cdot 5 < - 8 \cdot 5$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $5$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{4 x}{5} \cdot 5 < - 8 \cdot 5$

Step 4.1.1.2

Rewrite the expression.

$4 x < - 8 \cdot 5$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 8$ by $5$ .

$4 x < - 40$

Step 5

Divide each term in $4 x < - 40$ by $4$ and simplify.

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Step 5.1

Divide each term in $4 x < - 40$ by $4$ .

$\frac{4 x}{4} < \frac{- 40}{4}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $4$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{4 x}{4} < \frac{- 40}{4}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x < \frac{- 40}{4}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 40$ by $4$ .

$x < - 10$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < - 10$

Interval Notation:

$(- \infty, - 10)$