Algebra Examples

$- 8 x + 2 x - 16 < - 5 x + 7 x$

Step 1

Add $- 8 x$ and $2 x$ .

$- 6 x - 16 < - 5 x + 7 x$

Step 2

Add $- 5 x$ and $7 x$ .

$- 6 x - 16 < 2 x$

Step 3

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

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Step 3.1

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

$- 6 x - 16 - 2 x < 0$

Step 3.2

Subtract $2 x$ from $- 6 x$ .

$- 8 x - 16 < 0$

Step 4

Add $16$ to both sides of the inequality.

$- 8 x < 16$

Step 5

Divide each term in $- 8 x < 16$ by $- 8$ and simplify.

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Step 5.1

Divide each term in $- 8 x < 16$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 x}{- 8} > \frac{16}{- 8}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 8$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 8 x}{- 8} > \frac{16}{- 8}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x > \frac{16}{- 8}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $16$ by $- 8$ .

$x > - 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > - 2$

Interval Notation:

$(- 2, \infty)$