Algebra Examples

$x - 5 > 2 x + 3$

Step 1

Move all terms containing $x$ to the left side of the inequality.

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Step 1.1

Subtract $2 x$ from both sides of the inequality.

$x - 5 - 2 x > 3$

Step 1.2

Subtract $2 x$ from $x$ .

$- x - 5 > 3$

Step 2

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

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Step 2.1

Add $5$ to both sides of the inequality.

$- x > 3 + 5$

Step 2.2

Add $3$ and $5$ .

$- x > 8$

Step 3

Divide each term in $- x > 8$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- x > 8$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} < \frac{8}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} < \frac{8}{- 1}$

Step 3.2.2

Divide $x$ by $1$ .

$x < \frac{8}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $8$ by $- 1$ .

$x < - 8$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < - 8$

Interval Notation:

$(- \infty, - 8)$