Finite Math Examples

$- \frac{t}{5} + 7 > - 4$

Step 1

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

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Step 1.1

Subtract $7$ from both sides of the inequality.

$- \frac{t}{5} > - 4 - 7$

Step 1.2

Subtract $7$ from $- 4$ .

$- \frac{t}{5} > - 11$

Step 2

Divide each term in $- \frac{t}{5} > - 11$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- \frac{t}{5} > - 11$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{t}{5}}{- 1} < \frac{- 11}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{t}{5}}{1} < \frac{- 11}{- 1}$

Step 2.2.2

Divide $\frac{t}{5}$ by $1$ .

$\frac{t}{5} < \frac{- 11}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 11$ by $- 1$ .

$\frac{t}{5} < 11$

Step 3

Multiply both sides by $5$ .

$\frac{t}{5} \cdot 5 < 11 \cdot 5$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $5$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{t}{5} \cdot 5 < 11 \cdot 5$

Step 4.1.1.2

Rewrite the expression.

$t < 11 \cdot 5$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $11$ by $5$ .

$t < 55$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$t < 55$

Interval Notation:

$(- \infty, 55)$