Algebra Examples

$3 \geq 2 x$ or $x - 4 > 2$

Step 1

Simplify the first inequality.

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Step 1.1

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

$2 x \leq 3$ or $x - 4 > 2$

Step 1.2

Divide each term in $2 x \leq 3$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 x \leq 3$ by $2$ .

$\frac{2 x}{2} \leq \frac{3}{2}$ or $x - 4 > 2$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{3}{2}$ or $x - 4 > 2$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{3}{2}$ or $x - 4 > 2$

Step 2

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

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Step 2.1

Add $4$ to both sides of the inequality.

$x \leq \frac{3}{2}$ or $x > 2 + 4$

Step 2.2

Add $2$ and $4$ .

$x \leq \frac{3}{2}$ or $x > 6$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{3}{2} or x > 6$

Interval Notation:

$(- \infty, \frac{3}{2}] \cup (6, \infty)$

Step 4