Algebra Examples

$- \frac{1}{2} (16 x - 4) \leq 2 x - 18$

Step 1

Simplify $- \frac{1}{2} \cdot (16 x - 4)$ .

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Step 1.1

Rewrite.

$0 + 0 - \frac{1}{2} \cdot (16 x - 4) \leq 2 x - 18$

Step 1.2

Simplify by adding zeros.

$- \frac{1}{2} \cdot (16 x - 4) \leq 2 x - 18$

Step 1.3

Apply the distributive property.

$- \frac{1}{2} (16 x) - \frac{1}{2} \cdot - 4 \leq 2 x - 18$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{- 1}{2} (16 x) - \frac{1}{2} \cdot - 4 \leq 2 x - 18$

Step 1.4.2

Factor $2$ out of $16 x$ .

$\frac{- 1}{2} (2 (8 x)) - \frac{1}{2} \cdot - 4 \leq 2 x - 18$

Step 1.4.3

Cancel the common factor.

$\frac{- 1}{2} (2 (8 x)) - \frac{1}{2} \cdot - 4 \leq 2 x - 18$

Step 1.4.4

Rewrite the expression.

$- 1 (8 x) - \frac{1}{2} \cdot - 4 \leq 2 x - 18$

Step 1.5

Multiply $8$ by $- 1$ .

$- 8 x - \frac{1}{2} \cdot - 4 \leq 2 x - 18$

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$- 8 x + \frac{- 1}{2} \cdot - 4 \leq 2 x - 18$

Step 1.6.2

Factor $2$ out of $- 4$ .

$- 8 x + \frac{- 1}{2} \cdot (2 (- 2)) \leq 2 x - 18$

Step 1.6.3

Cancel the common factor.

$- 8 x + \frac{- 1}{2} \cdot (2 \cdot - 2) \leq 2 x - 18$

Step 1.6.4

Rewrite the expression.

$- 8 x - 1 \cdot - 2 \leq 2 x - 18$

Step 1.7

Multiply $- 1$ by $- 2$ .

$- 8 x + 2 \leq 2 x - 18$

Step 2

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

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Step 2.1

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

$- 8 x + 2 - 2 x \leq - 18$

Step 2.2

Subtract $2 x$ from $- 8 x$ .

$- 10 x + 2 \leq - 18$

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.

$- 10 x \leq - 18 - 2$

Step 3.2

Subtract $2$ from $- 18$ .

$- 10 x \leq - 20$

Step 4

Divide each term in $- 10 x \leq - 20$ by $- 10$ and simplify.

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Step 4.1

Divide each term in $- 10 x \leq - 20$ by $- 10$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 10 x}{- 10} \geq \frac{- 20}{- 10}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 10$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 10 x}{- 10} \geq \frac{- 20}{- 10}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{- 20}{- 10}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 20$ by $- 10$ .

$x \geq 2$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \geq 2$

Interval Notation:

$[2, \infty)$