Algebra Examples

$1 < \frac{3 x}{4}$

Step 1

Multiply both sides by $4$ .

$1 \cdot 4 < \frac{3 x}{4} \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Multiply $4$ by $1$ .

$4 < \frac{3 x}{4} \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$4 < \frac{3 x}{4} \cdot 4$

Step 2.2.1.2

Rewrite the expression.

$4 < 3 x$

Step 3

Solve for $x$ .

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Step 3.1

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

$3 x > 4$

Step 3.2

Divide each term in $3 x > 4$ by $3$ and simplify.

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Step 3.2.1

Divide each term in $3 x > 4$ by $3$ .

$\frac{3 x}{3} > \frac{4}{3}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $3$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} > \frac{4}{3}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x > \frac{4}{3}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{4}{3}$

Interval Notation:

$(\frac{4}{3}, \infty)$