Algebra Examples

$3 - \frac{1}{2} x \leq 11$

Step 1

Combine $x$ and $\frac{1}{2}$ .

$3 - \frac{x}{2} \leq 11$

Step 2

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

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Step 2.1

Subtract $3$ from both sides of the inequality.

$- \frac{x}{2} \leq 11 - 3$

Step 2.2

Subtract $3$ from $11$ .

$- \frac{x}{2} \leq 8$

Step 3

Divide each term in $- \frac{x}{2} \leq 8$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- \frac{x}{2} \leq 8$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{x}{2}}{- 1} \geq \frac{8}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{x}{2}}{1} \geq \frac{8}{- 1}$

Step 3.2.2

Divide $\frac{x}{2}$ by $1$ .

$\frac{x}{2} \geq \frac{8}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $8$ by $- 1$ .

$\frac{x}{2} \geq - 8$

Step 4

Multiply both sides by $2$ .

$\frac{x}{2} \cdot 2 \geq - 8 \cdot 2$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{x}{2} \cdot 2 \geq - 8 \cdot 2$

Step 5.1.1.2

Rewrite the expression.

$x \geq - 8 \cdot 2$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 8$ by $2$ .

$x \geq - 16$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 16$

Interval Notation:

$[- 16, \infty)$