Algebra Examples

$\frac{3 x}{2} - 2 > 7$

Step 1

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

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Step 1.1

Add $2$ to both sides of the inequality.

$\frac{3 x}{2} > 7 + 2$

Step 1.2

Add $7$ and $2$ .

$\frac{3 x}{2} > 9$

Step 2

Multiply both sides by $2$ .

$\frac{3 x}{2} \cdot 2 > 9 \cdot 2$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{3 x}{2} \cdot 2 > 9 \cdot 2$

Step 3.1.1.2

Rewrite the expression.

$3 x > 9 \cdot 2$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $9$ by $2$ .

$3 x > 18$

Step 4

Divide each term in $3 x > 18$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 x > 18$ by $3$ .

$\frac{3 x}{3} > \frac{18}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 x}{3} > \frac{18}{3}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x > \frac{18}{3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $18$ by $3$ .

$x > 6$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > 6$

Interval Notation:

$(6, \infty)$