Algebra Examples

$- 2 \leq \frac{3 x - 1}{8} \leq 0$

Step 1

Solve $- 2 \leq \frac{3 x - 1}{8}$ for $x$ .

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Step 1.1

Multiply both sides by $8$ .

$- 2 \cdot 8 \leq \frac{3 x - 1}{8} \cdot 8$

Step 1.2

Simplify.

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Step 1.2.1

Simplify the left side.

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Step 1.2.1.1

Multiply $- 2$ by $8$ .

$- 16 \leq \frac{3 x - 1}{8} \cdot 8$

Step 1.2.2

Simplify the right side.

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Step 1.2.2.1

Cancel the common factor of $8$ .

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Step 1.2.2.1.1

Cancel the common factor.

$- 16 \leq \frac{3 x - 1}{8} \cdot 8$

Step 1.2.2.1.2

Rewrite the expression.

$- 16 \leq 3 x - 1$

Step 1.3

Solve for $x$ .

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Step 1.3.1

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

$3 x - 1 \geq - 16$

Step 1.3.2

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

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Step 1.3.2.1

Add $1$ to both sides of the inequality.

$3 x \geq - 16 + 1$

Step 1.3.2.2

Add $- 16$ and $1$ .

$3 x \geq - 15$

Step 1.3.3

Divide each term in $3 x \geq - 15$ by $3$ and simplify.

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Step 1.3.3.1

Divide each term in $3 x \geq - 15$ by $3$ .

$\frac{3 x}{3} \geq \frac{- 15}{3}$

Step 1.3.3.2

Simplify the left side.

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Step 1.3.3.2.1

Cancel the common factor of $3$ .

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Step 1.3.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} \geq \frac{- 15}{3}$

Step 1.3.3.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{- 15}{3}$

Step 1.3.3.3

Simplify the right side.

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Step 1.3.3.3.1

Divide $- 15$ by $3$ .

$x \geq - 5$

Step 2

Solve $\frac{3 x - 1}{8} \leq 0$ for $x$ .

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Step 2.1

Multiply both sides by $8$ .

$\frac{3 x - 1}{8} \cdot 8 \leq 0 \cdot 8$

Step 2.2

Simplify.

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Cancel the common factor of $8$ .

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Step 2.2.1.1.1

Cancel the common factor.

$\frac{3 x - 1}{8} \cdot 8 \leq 0 \cdot 8$

Step 2.2.1.1.2

Rewrite the expression.

$3 x - 1 \leq 0 \cdot 8$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Multiply $0$ by $8$ .

$3 x - 1 \leq 0$

Step 2.3

Solve for $x$ .

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Step 2.3.1

Add $1$ to both sides of the inequality.

$3 x \leq 1$

Step 2.3.2

Divide each term in $3 x \leq 1$ by $3$ and simplify.

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Step 2.3.2.1

Divide each term in $3 x \leq 1$ by $3$ .

$\frac{3 x}{3} \leq \frac{1}{3}$

Step 2.3.2.2

Simplify the left side.

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Step 2.3.2.2.1

Cancel the common factor of $3$ .

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Step 2.3.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} \leq \frac{1}{3}$

Step 2.3.2.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{1}{3}$

Step 3

Find the intersection of $x \geq - 5$ and $x \leq \frac{1}{3}$ .

$- 5 \leq x \leq \frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 5 \leq x \leq \frac{1}{3}$

Interval Notation:

$[- 5, \frac{1}{3}]$

Step 5