Algebra Examples

$- 4 \leq 2 x - 6 \leq 12$

Step 1

Solve $- 4 \leq 2 x - 6$ for $x$ .

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Step 1.1

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

$2 x - 6 \geq - 4$

Step 1.2

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

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Step 1.2.1

Add $6$ to both sides of the inequality.

$2 x \geq - 4 + 6$

Step 1.2.2

Add $- 4$ and $6$ .

$2 x \geq 2$

Step 1.3

Divide each term in $2 x \geq 2$ by $2$ and simplify.

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Step 1.3.1

Divide each term in $2 x \geq 2$ by $2$ .

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

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $2$ .

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Step 1.3.2.1.1

Cancel the common factor.

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

Step 1.3.2.1.2

Divide $x$ by $1$ .

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

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Divide $2$ by $2$ .

$x \geq 1$

Step 2

Solve $2 x - 6 \leq 12$ for $x$ .

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Step 2.1

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

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Step 2.1.1

Add $6$ to both sides of the inequality.

$2 x \leq 12 + 6$

Step 2.1.2

Add $12$ and $6$ .

$2 x \leq 18$

Step 2.2

Divide each term in $2 x \leq 18$ by $2$ and simplify.

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Step 2.2.1

Divide each term in $2 x \leq 18$ by $2$ .

$\frac{2 x}{2} \leq \frac{18}{2}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{18}{2}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{18}{2}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $18$ by $2$ .

$x \leq 9$

Step 3

Find the intersection of $x \geq 1$ and $x \leq 9$ .

$1 \leq x \leq 9$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$1 \leq x \leq 9$

Interval Notation:

$[1, 9]$

Step 5