Algebra Examples

$86 \leq - 4 (1 - 5 x) - 2 x$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$- 4 (1 - 5 x) - 2 x \geq 86$

Step 2

Simplify $- 4 (1 - 5 x) - 2 x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 4 \cdot 1 - 4 (- 5 x) - 2 x \geq 86$

Step 2.1.2

Multiply $- 4$ by $1$ .

$- 4 - 4 (- 5 x) - 2 x \geq 86$

Step 2.1.3

Multiply $- 5$ by $- 4$ .

$- 4 + 20 x - 2 x \geq 86$

Step 2.2

Subtract $2 x$ from $20 x$ .

$- 4 + 18 x \geq 86$

Step 3

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

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Step 3.1

Add $4$ to both sides of the inequality.

$18 x \geq 86 + 4$

Step 3.2

Add $86$ and $4$ .

$18 x \geq 90$

Step 4

Divide each term in $18 x \geq 90$ by $18$ and simplify.

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Step 4.1

Divide each term in $18 x \geq 90$ by $18$ .

$\frac{18 x}{18} \geq \frac{90}{18}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $18$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{18 x}{18} \geq \frac{90}{18}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{90}{18}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $90$ by $18$ .

$x \geq 5$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \geq 5$

Interval Notation:

$[5, \infty)$