Algebra Examples

$- \frac{1}{2} x > 6$

Step 1

Multiply each term in $- \frac{1}{2} x > 6$ by $- 2$ to eliminate the fractions.

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Step 1.1

Multiply each term in $- \frac{1}{2} x > 6$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$- \frac{1}{2} x \cdot - 2 < 6 \cdot - 2$

Step 1.2

Simplify the left side.

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Step 1.2.1

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

$- \frac{x}{2} \cdot - 2 < 6 \cdot - 2$

Step 1.2.2

Cancel the common factor of $2$ .

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Step 1.2.2.1

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$\frac{- x}{2} \cdot - 2 < 6 \cdot - 2$

Step 1.2.2.2

Factor $2$ out of $- 2$ .

$\frac{- x}{2} \cdot (2 (- 1)) < 6 \cdot - 2$

Step 1.2.2.3

Cancel the common factor.

$\frac{- x}{2} \cdot (2 \cdot - 1) < 6 \cdot - 2$

Step 1.2.2.4

Rewrite the expression.

$- x \cdot - 1 < 6 \cdot - 2$

Step 1.2.3

Multiply.

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Step 1.2.3.1

Multiply $- 1$ by $- 1$ .

$1 x < 6 \cdot - 2$

Step 1.2.3.2

Multiply $x$ by $1$ .

$x < 6 \cdot - 2$

Step 1.3

Simplify the right side.

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Step 1.3.1

Multiply $6$ by $- 2$ .

$x < - 12$

Step 2

Use the inequality $x < - 12$ to build the set notation.

${x | x < - 12}$

Step 3