Algebra Examples

$0.36 w \leq 0.54$ and $- \frac{1}{2} w > 3$

Step 1

Divide each term in $0.36 w \leq 0.54$ by $0.36$ and simplify.

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Step 1.1

Divide each term in $0.36 w \leq 0.54$ by $0.36$ .

$\frac{0.36 w}{0.36} \leq \frac{0.54}{0.36}$ and $- \frac{1}{2} w > 3$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $0.36$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{0.36 w}{0.36} \leq \frac{0.54}{0.36}$ and $- \frac{1}{2} w > 3$

Step 1.2.1.2

Divide $w$ by $1$ .

$w \leq \frac{0.54}{0.36}$ and $- \frac{1}{2} w > 3$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $0.54$ by $0.36$ .

$w \leq 1.5$ and $- \frac{1}{2} w > 3$

Step 2

Multiply each term in $- \frac{1}{2} w > 3$ by $- 2$ to eliminate the fractions.

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Step 2.1

Multiply each term in $- \frac{1}{2} w > 3$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$w \leq 1.5$ and $- \frac{1}{2} w \cdot - 2 < 3 \cdot - 2$

Step 2.2

Simplify the left side.

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Step 2.2.1

Combine $w$ and $\frac{1}{2}$ .

$w \leq 1.5$ and $- \frac{w}{2} \cdot - 2 < 3 \cdot - 2$

Step 2.2.2

Cancel the common factor of $2$ .

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Step 2.2.2.1

Move the leading negative in $- \frac{w}{2}$ into the numerator.

$w \leq 1.5$ and $\frac{- w}{2} \cdot - 2 < 3 \cdot - 2$

Step 2.2.2.2

Factor $2$ out of $- 2$ .

$w \leq 1.5$ and $\frac{- w}{2} \cdot (2 (- 1)) < 3 \cdot - 2$

Step 2.2.2.3

Cancel the common factor.

$w \leq 1.5$ and $\frac{- w}{2} \cdot (2 \cdot - 1) < 3 \cdot - 2$

Step 2.2.2.4

Rewrite the expression.

$w \leq 1.5$ and $- w \cdot - 1 < 3 \cdot - 2$

Step 2.2.3

Multiply.

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Step 2.2.3.1

Multiply $- 1$ by $- 1$ .

$w \leq 1.5$ and $1 w < 3 \cdot - 2$

Step 2.2.3.2

Multiply $w$ by $1$ .

$w \leq 1.5$ and $w < 3 \cdot - 2$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply $3$ by $- 2$ .

$w \leq 1.5$ and $w < - 6$

Step 3

The intersection consists of the elements that are contained in both intervals.

$w < - 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$w < - 6$

Interval Notation:

$(- \infty, - 6)$

Step 5