Pre-Algebra Examples

$\frac{4 x - 7}{3} < \frac{19}{4}$

Step 1

Multiply both sides by $3$ .

$\frac{4 x - 7}{3} \cdot 3 < \frac{19}{4} \cdot 3$

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 $3$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{4 x - 7}{3} \cdot 3 < \frac{19}{4} \cdot 3$

Step 2.1.1.2

Rewrite the expression.

$4 x - 7 < \frac{19}{4} \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $\frac{19}{4} \cdot 3$ .

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Step 2.2.1.1

Combine $\frac{19}{4}$ and $3$ .

$4 x - 7 < \frac{19 \cdot 3}{4}$

Step 2.2.1.2

Multiply $19$ by $3$ .

$4 x - 7 < \frac{57}{4}$

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 $7$ to both sides of the inequality.

$4 x < \frac{57}{4} + 7$

Step 3.1.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$4 x < \frac{57}{4} + 7 \cdot \frac{4}{4}$

Step 3.1.3

Combine $7$ and $\frac{4}{4}$ .

$4 x < \frac{57}{4} + \frac{7 \cdot 4}{4}$

Step 3.1.4

Combine the numerators over the common denominator.

$4 x < \frac{57 + 7 \cdot 4}{4}$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Multiply $7$ by $4$ .

$4 x < \frac{57 + 28}{4}$

Step 3.1.5.2

Add $57$ and $28$ .

$4 x < \frac{85}{4}$

Step 3.2

Divide each term in $4 x < \frac{85}{4}$ by $4$ and simplify.

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Step 3.2.1

Divide each term in $4 x < \frac{85}{4}$ by $4$ .

$\frac{4 x}{4} < \frac{\frac{85}{4}}{4}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $4$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} < \frac{\frac{85}{4}}{4}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x < \frac{\frac{85}{4}}{4}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x < \frac{85}{4} \cdot \frac{1}{4}$

Step 3.2.3.2

Multiply $\frac{85}{4} \cdot \frac{1}{4}$ .

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Step 3.2.3.2.1

Multiply $\frac{85}{4}$ by $\frac{1}{4}$ .

$x < \frac{85}{4 \cdot 4}$

Step 3.2.3.2.2

Multiply $4$ by $4$ .

$x < \frac{85}{16}$

Step 4