Pre-Algebra Examples

$\frac{1}{4} \cdot (8 y + 4) + \frac{1}{2} \cdot (4 y - 6) < 18$

Step 1

Simplify $\frac{1}{4} \cdot (8 y + 4) + \frac{1}{2} \cdot (4 y - 6)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{1}{4} (8 y) + \frac{1}{4} \cdot 4 + \frac{1}{2} \cdot (4 y - 6) < 18$

Step 1.1.2

Cancel the common factor of $4$ .

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Step 1.1.2.1

Factor $4$ out of $8 y$ .

$\frac{1}{4} (4 (2 y)) + \frac{1}{4} \cdot 4 + \frac{1}{2} \cdot (4 y - 6) < 18$

Step 1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 (2 y)) + \frac{1}{4} \cdot 4 + \frac{1}{2} \cdot (4 y - 6) < 18$

Step 1.1.2.3

Rewrite the expression.

$2 y + \frac{1}{4} \cdot 4 + \frac{1}{2} \cdot (4 y - 6) < 18$

Step 1.1.3

Cancel the common factor of $4$ .

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Step 1.1.3.1

Cancel the common factor.

$2 y + \frac{1}{4} \cdot 4 + \frac{1}{2} \cdot (4 y - 6) < 18$

Step 1.1.3.2

Rewrite the expression.

$2 y + 1 + \frac{1}{2} \cdot (4 y - 6) < 18$

Step 1.1.4

Apply the distributive property.

$2 y + 1 + \frac{1}{2} (4 y) + \frac{1}{2} \cdot - 6 < 18$

Step 1.1.5

Cancel the common factor of $2$ .

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Step 1.1.5.1

Factor $2$ out of $4 y$ .

$2 y + 1 + \frac{1}{2} (2 (2 y)) + \frac{1}{2} \cdot - 6 < 18$

Step 1.1.5.2

Cancel the common factor.

$2 y + 1 + \frac{1}{2} (2 (2 y)) + \frac{1}{2} \cdot - 6 < 18$

Step 1.1.5.3

Rewrite the expression.

$2 y + 1 + 2 y + \frac{1}{2} \cdot - 6 < 18$

Step 1.1.6

Cancel the common factor of $2$ .

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Step 1.1.6.1

Factor $2$ out of $- 6$ .

$2 y + 1 + 2 y + \frac{1}{2} \cdot (2 (- 3)) < 18$

Step 1.1.6.2

Cancel the common factor.

$2 y + 1 + 2 y + \frac{1}{2} \cdot (2 \cdot - 3) < 18$

Step 1.1.6.3

Rewrite the expression.

$2 y + 1 + 2 y - 3 < 18$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Add $2 y$ and $2 y$ .

$4 y + 1 - 3 < 18$

Step 1.2.2

Subtract $3$ from $1$ .

$4 y - 2 < 18$

Step 2

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

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Step 2.1

Add $2$ to both sides of the inequality.

$4 y < 18 + 2$

Step 2.2

Add $18$ and $2$ .

$4 y < 20$

Step 3

Divide each term in $4 y < 20$ by $4$ and simplify.

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Step 3.1

Divide each term in $4 y < 20$ by $4$ .

$\frac{4 y}{4} < \frac{20}{4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{4 y}{4} < \frac{20}{4}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y < \frac{20}{4}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $20$ by $4$ .

$y < 5$

Step 4