Algebra Examples

$- \frac{3}{8} x - 2 < - 13 + 17$

Step 1

Simplify each term.

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Step 1.1

Combine $x$ and $\frac{3}{8}$ .

$- \frac{x \cdot 3}{8} - 2 < - 13 + 17$

Step 1.2

Move $3$ to the left of $x$ .

$- \frac{3 x}{8} - 2 < - 13 + 17$

Step 2

Add $- 13$ and $17$ .

$- \frac{3 x}{8} - 2 < 4$

Step 3

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

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Step 3.1

Add $2$ to both sides of the inequality.

$- \frac{3 x}{8} < 4 + 2$

Step 3.2

Add $4$ and $2$ .

$- \frac{3 x}{8} < 6$

Step 4

Divide each term in $- \frac{3 x}{8} < 6$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- \frac{3 x}{8} < 6$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{3 x}{8}}{- 1} > \frac{6}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{3 x}{8}}{1} > \frac{6}{- 1}$

Step 4.2.2

Divide $\frac{3 x}{8}$ by $1$ .

$\frac{3 x}{8} > \frac{6}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $6$ by $- 1$ .

$\frac{3 x}{8} > - 6$

Step 5

Multiply both sides by $8$ .

$\frac{3 x}{8} \cdot 8 > - 6 \cdot 8$

Step 6

Simplify.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $8$ .

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Step 6.1.1.1

Cancel the common factor.

$\frac{3 x}{8} \cdot 8 > - 6 \cdot 8$

Step 6.1.1.2

Rewrite the expression.

$3 x > - 6 \cdot 8$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $- 6$ by $8$ .

$3 x > - 48$

Step 7

Divide each term in $3 x > - 48$ by $3$ and simplify.

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Step 7.1

Divide each term in $3 x > - 48$ by $3$ .

$\frac{3 x}{3} > \frac{- 48}{3}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $3$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{3 x}{3} > \frac{- 48}{3}$

Step 7.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 48}{3}$

Step 7.3

Simplify the right side.

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Step 7.3.1

Divide $- 48$ by $3$ .

$x > - 16$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$x > - 16$

Interval Notation:

$(- 16, \infty)$