Pre-Algebra Examples

$\frac{3 x - 1}{4} < 8$

Step 1

Multiply both sides by $4$ .

$\frac{3 x - 1}{4} \cdot 4 < 8 \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $4$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{3 x - 1}{4} \cdot 4 < 8 \cdot 4$

Step 2.1.1.2

Rewrite the expression.

$3 x - 1 < 8 \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $8$ by $4$ .

$3 x - 1 < 32$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Add $1$ to both sides of the inequality.

$3 x < 32 + 1$

Step 3.1.2

Add $32$ and $1$ .

$3 x < 33$

Step 3.2

Divide each term in $3 x < 33$ by $3$ and simplify.

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Step 3.2.1

Divide each term in $3 x < 33$ by $3$ .

$\frac{3 x}{3} < \frac{33}{3}$

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.

$\frac{3 x}{3} < \frac{33}{3}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x < \frac{33}{3}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $33$ by $3$ .

$x < 11$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 11$

Interval Notation:

$(- \infty, 11)$