Pre-Algebra Examples

$11 x - 10 x + 2 \leq 8 + 3 x$

Step 1

Subtract $10 x$ from $11 x$ .

$x + 2 \leq 8 + 3 x$

Step 2

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

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Step 2.1

Subtract $3 x$ from both sides of the inequality.

$x + 2 - 3 x \leq 8$

Step 2.2

Subtract $3 x$ from $x$ .

$- 2 x + 2 \leq 8$

Step 3

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

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Step 3.1

Subtract $2$ from both sides of the inequality.

$- 2 x \leq 8 - 2$

Step 3.2

Subtract $2$ from $8$ .

$- 2 x \leq 6$

Step 4

Divide each term in $- 2 x \leq 6$ by $- 2$ and simplify.

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Step 4.1

Divide each term in $- 2 x \leq 6$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \geq \frac{6}{- 2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} \geq \frac{6}{- 2}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{6}{- 2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $6$ by $- 2$ .

$x \geq - 3$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 3$

Interval Notation:

$[- 3, \infty)$