Algebra Examples

$\frac{3 y - 4}{0.2} - 8 > 12$

Step 1

Simplify $\frac{3 y - 4}{0.2} - 8$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Factor $1$ out of $3 y$ .

$\frac{1 (3 y) - 4}{0.2} - 8 > 12$

Step 1.1.2

Rewrite $- 4$ as $1 (- 4)$ .

$\frac{1 (3 y) + 1 (- 4)}{0.2} - 8 > 12$

Step 1.1.3

Factor $1$ out of $1 (3 y) + 1 (- 4)$ .

$\frac{1 (3 y - 4)}{0.2} - 8 > 12$

Step 1.1.4

Factor $0.2$ out of $0.2$ .

$\frac{1 (3 y - 4)}{0.2 (1)} - 8 > 12$

Step 1.1.5

Separate fractions.

$\frac{1}{0.2} \cdot \frac{3 y - 4}{1} - 8 > 12$

Step 1.1.6

Divide $1$ by $0.2$ .

$5 \frac{3 y - 4}{1} - 8 > 12$

Step 1.1.7

Divide $3 y - 4$ by $1$ .

$5 (3 y - 4) - 8 > 12$

Step 1.1.8

Apply the distributive property.

$5 (3 y) + 5 \cdot - 4 - 8 > 12$

Step 1.1.9

Multiply $3$ by $5$ .

$15 y + 5 \cdot - 4 - 8 > 12$

Step 1.1.10

Multiply $5$ by $- 4$ .

$15 y - 20 - 8 > 12$

$15 y - 20 - 8 > 12$

Step 1.2

Subtract $8$ from $- 20$ .

$15 y - 28 > 12$

$15 y - 28 > 12$

Step 2

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

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Step 2.1

Add $28$ to both sides of the inequality.

$15 y > 12 + 28$

Step 2.2

Add $12$ and $28$ .

$15 y > 40$

$15 y > 40$

Step 3

Divide each term in $15 y > 40$ by $15$ and simplify.

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Step 3.1

Divide each term in $15 y > 40$ by $15$ .

$\frac{15 y}{15} > \frac{40}{15}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $15$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{15 y}{15} > \frac{40}{15}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y > \frac{40}{15}$

$y > \frac{40}{15}$

$y > \frac{40}{15}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $40$ and $15$ .

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Step 3.3.1.1

Factor $5$ out of $40$ .

$y > \frac{5 (8)}{15}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $5$ out of $15$ .

$y > \frac{5 \cdot 8}{5 \cdot 3}$

Step 3.3.1.2.2

Cancel the common factor.

$y > \frac{5 \cdot 8}{5 \cdot 3}$

Step 3.3.1.2.3

Rewrite the expression.

$y > \frac{8}{3}$

$y > \frac{8}{3}$

$y > \frac{8}{3}$

$y > \frac{8}{3}$

$y > \frac{8}{3}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$y > \frac{8}{3}$

Interval Notation:

$(\frac{8}{3}, \infty)$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$