Algebra Examples

$\frac{1}{4} (x - 3) \leq - 2$

Step 1

Multiply each term in $\frac{1}{4} \cdot (x - 3) \leq - 2$ by $4$ to eliminate the fractions.

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Step 1.1

Multiply each term in $\frac{1}{4} \cdot (x - 3) \leq - 2$ by $4$ .

$\frac{1}{4} \cdot (x - 3) \cdot 4 \leq - 2 \cdot 4$

Step 1.2

Simplify the left side.

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Step 1.2.1

Apply the distributive property.

$(\frac{1}{4} x + \frac{1}{4} \cdot - 3) \cdot 4 \leq - 2 \cdot 4$

Step 1.2.2

Combine $\frac{1}{4}$ and $x$ .

$(\frac{x}{4} + \frac{1}{4} \cdot - 3) \cdot 4 \leq - 2 \cdot 4$

Step 1.2.3

Combine $\frac{1}{4}$ and $- 3$ .

$(\frac{x}{4} + \frac{- 3}{4}) \cdot 4 \leq - 2 \cdot 4$

Step 1.2.4

Move the negative in front of the fraction.

$(\frac{x}{4} - \frac{3}{4}) \cdot 4 \leq - 2 \cdot 4$

Step 1.2.5

Apply the distributive property.

$\frac{x}{4} \cdot 4 - \frac{3}{4} \cdot 4 \leq - 2 \cdot 4$

Step 1.2.6

Cancel the common factor of $4$ .

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Step 1.2.6.1

Cancel the common factor.

$\frac{x}{4} \cdot 4 - \frac{3}{4} \cdot 4 \leq - 2 \cdot 4$

Step 1.2.6.2

Rewrite the expression.

$x - \frac{3}{4} \cdot 4 \leq - 2 \cdot 4$

Step 1.2.7

Cancel the common factor of $4$ .

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Step 1.2.7.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$x + \frac{- 3}{4} \cdot 4 \leq - 2 \cdot 4$

Step 1.2.7.2

Cancel the common factor.

$x + \frac{- 3}{4} \cdot 4 \leq - 2 \cdot 4$

Step 1.2.7.3

Rewrite the expression.

$x - 3 \leq - 2 \cdot 4$

Step 1.3

Simplify the right side.

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Step 1.3.1

Multiply $- 2$ by $4$ .

$x - 3 \leq - 8$

Step 2

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

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Step 2.1

Add $3$ to both sides of the inequality.

$x \leq - 8 + 3$

Step 2.2

Add $- 8$ and $3$ .

$x \leq - 5$

Step 3