Algebra Examples

$\frac{t}{- 3.2} < 5$

Step 1

Multiply both sides by $- 3.2$ .

$\frac{t}{- 3.2} \cdot - 3.2 > 5 \cdot - 3.2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{t}{- 3.2} \cdot - 3.2$ .

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Step 2.1.1.1

Cancel the common factor of $3.2$ .

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Step 2.1.1.1.1

Factor $3.2$ out of $- 3.2$ .

$\frac{t}{3.2 (- 1)} \cdot - 3.2 > 5 \cdot - 3.2$

Step 2.1.1.1.2

Factor $3.2$ out of $- 3.2$ .

$\frac{t}{3.2 \cdot - 1} \cdot (3.2 \cdot - 1) > 5 \cdot - 3.2$

Step 2.1.1.1.3

Cancel the common factor.

$\frac{t}{3.2 \cdot - 1} \cdot (3.2 \cdot - 1) > 5 \cdot - 3.2$

Step 2.1.1.1.4

Rewrite the expression.

$\frac{t}{- 1} \cdot - 1 > 5 \cdot - 3.2$

Step 2.1.1.2

Combine $\frac{t}{- 1}$ and $- 1$ .

$\frac{t \cdot - 1}{- 1} > 5 \cdot - 3.2$

Step 2.1.1.3

Simplify the expression.

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Step 2.1.1.3.1

Move the negative one from the denominator of $\frac{t \cdot - 1}{- 1}$ .

$- 1 \cdot (t \cdot - 1) > 5 \cdot - 3.2$

Step 2.1.1.3.2

Rewrite $- 1 \cdot (t \cdot - 1)$ as $- (t \cdot - 1)$ .

$- (t \cdot - 1) > 5 \cdot - 3.2$

Step 2.1.1.3.3

Move $- 1$ to the left of $t$ .

$- (- 1 \cdot t) > 5 \cdot - 3.2$

Step 2.1.1.3.4

Rewrite $- 1 t$ as $- t$ .

$- - t > 5 \cdot - 3.2$

Step 2.1.1.4

Multiply $- - t$ .

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Step 2.1.1.4.1

Multiply $- 1$ by $- 1$ .

$1 t > 5 \cdot - 3.2$

Step 2.1.1.4.2

Multiply $t$ by $1$ .

$t > 5 \cdot - 3.2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $5$ by $- 3.2$ .

$t > - 16$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$t > - 16$

Interval Notation:

$(- 16, \infty)$