Algebra Examples

$\frac{1}{4} (8 y + 4) - 27 < - \frac{1}{4} (8 y - 8)$

Step 1

Solve $y < 7$ .

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Step 1.1

Simplify $\frac{1}{4} (8 y + 4) - 27$ .

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Apply the distributive property.

$\frac{1}{4} (8 y) + \frac{1}{4} \cdot 4 - 27 < - \frac{1}{4} (8 y - 8)$

Step 1.1.1.2

Cancel the common factor of $4$ .

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Step 1.1.1.2.1

Factor $4$ out of $8 y$ .

$\frac{1}{4} (4 (2 y)) + \frac{1}{4} \cdot 4 - 27 < - \frac{1}{4} (8 y - 8)$

Step 1.1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 (2 y)) + \frac{1}{4} \cdot 4 - 27 < - \frac{1}{4} (8 y - 8)$

Step 1.1.1.2.3

Rewrite the expression.

$2 y + \frac{1}{4} \cdot 4 - 27 < - \frac{1}{4} (8 y - 8)$

Step 1.1.1.3

Cancel the common factor of $4$ .

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Step 1.1.1.3.1

Cancel the common factor.

$2 y + \frac{1}{4} \cdot 4 - 27 < - \frac{1}{4} (8 y - 8)$

Step 1.1.1.3.2

Rewrite the expression.

$2 y + 1 - 27 < - \frac{1}{4} (8 y - 8)$

Step 1.1.2

Subtract $27$ from $1$ .

$2 y - 26 < - \frac{1}{4} (8 y - 8)$

Step 1.2

Simplify $- \frac{1}{4} (8 y - 8)$ .

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Step 1.2.1

Apply the distributive property.

$2 y - 26 < - \frac{1}{4} (8 y) - \frac{1}{4} \cdot - 8$

Step 1.2.2

Cancel the common factor of $4$ .

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Step 1.2.2.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$2 y - 26 < \frac{- 1}{4} (8 y) - \frac{1}{4} \cdot - 8$

Step 1.2.2.2

Factor $4$ out of $8 y$ .

$2 y - 26 < \frac{- 1}{4} (4 (2 y)) - \frac{1}{4} \cdot - 8$

Step 1.2.2.3

Cancel the common factor.

$2 y - 26 < \frac{- 1}{4} (4 (2 y)) - \frac{1}{4} \cdot - 8$

Step 1.2.2.4

Rewrite the expression.

$2 y - 26 < - 1 (2 y) - \frac{1}{4} \cdot - 8$

Step 1.2.3

Multiply $2$ by $- 1$ .

$2 y - 26 < - 2 y - \frac{1}{4} \cdot - 8$

Step 1.2.4

Cancel the common factor of $4$ .

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Step 1.2.4.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$2 y - 26 < - 2 y + \frac{- 1}{4} \cdot - 8$

Step 1.2.4.2

Factor $4$ out of $- 8$ .

$2 y - 26 < - 2 y + \frac{- 1}{4} \cdot (4 (- 2))$

Step 1.2.4.3

Cancel the common factor.

$2 y - 26 < - 2 y + \frac{- 1}{4} \cdot (4 \cdot - 2)$

Step 1.2.4.4

Rewrite the expression.

$2 y - 26 < - 2 y - 1 \cdot - 2$

Step 1.2.5

Multiply $- 1$ by $- 2$ .

$2 y - 26 < - 2 y + 2$

Step 1.3

Move all terms containing $y$ to the left side of the inequality.

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Step 1.3.1

Add $2 y$ to both sides of the inequality.

$2 y - 26 + 2 y < 2$

Step 1.3.2

Add $2 y$ and $2 y$ .

$4 y - 26 < 2$

Step 1.4

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

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Step 1.4.1

Add $26$ to both sides of the inequality.

$4 y < 2 + 26$

Step 1.4.2

Add $2$ and $26$ .

$4 y < 28$

Step 1.5

Divide each term in $4 y < 28$ by $4$ and simplify.

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Step 1.5.1

Divide each term in $4 y < 28$ by $4$ .

$\frac{4 y}{4} < \frac{28}{4}$

Step 1.5.2

Simplify the left side.

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Step 1.5.2.1

Cancel the common factor of $4$ .

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Step 1.5.2.1.1

Cancel the common factor.

$\frac{4 y}{4} < \frac{28}{4}$

Step 1.5.2.1.2

Divide $y$ by $1$ .

$y < \frac{28}{4}$

Step 1.5.3

Simplify the right side.

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Step 1.5.3.1

Divide $28$ by $4$ .

$y < 7$

Step 2

Use the inequality $y < 7$ to build the set notation.

${y | y < 7}$

Step 3