Algebra Examples

$0.5 x + 2 > - 2.5$ $0.4 x - 8 < - 2$

Step 1

Solve $0.5 x + 2 > - 2.5$ for $x$ .

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Step 1.1

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

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Step 1.1.1

Subtract $2$ from both sides of the inequality.

$0.5 x > - 2.5 - 2$

Step 1.1.2

Subtract $2$ from $- 2.5$ .

$0.5 x > - 4.5$

Step 1.2

Divide each term in $0.5 x > - 4.5$ by $0.5$ and simplify.

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Step 1.2.1

Divide each term in $0.5 x > - 4.5$ by $0.5$ .

$\frac{0.5 x}{0.5} > \frac{- 4.5}{0.5}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $0.5$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{0.5 x}{0.5} > \frac{- 4.5}{0.5}$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 4.5}{0.5}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $- 4.5$ by $0.5$ .

$x > - 9$

Step 2

Solve $0.4 x - 8 < - 2$ for $x$ .

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Step 2.1

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

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Step 2.1.1

Add $8$ to both sides of the inequality.

$0.4 x < - 2 + 8$

Step 2.1.2

Add $- 2$ and $8$ .

$0.4 x < 6$

Step 2.2

Divide each term in $0.4 x < 6$ by $0.4$ and simplify.

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Step 2.2.1

Divide each term in $0.4 x < 6$ by $0.4$ .

$\frac{0.4 x}{0.4} < \frac{6}{0.4}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $0.4$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{0.4 x}{0.4} < \frac{6}{0.4}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x < \frac{6}{0.4}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $6$ by $0.4$ .

$x < 15$

Step 3

Find the intersection of $x > - 9$ and $x < 15$ .

$- 9 < x < 15$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 9 < x < 15$

Interval Notation:

$(- 9, 15)$

Step 5