Finite Math Examples

$4 (3 t + 4) > 2 (11 t + 11)$

Step 1

Simplify $4 (3 t + 4)$ .

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Step 1.1

Rewrite.

$0 + 0 + 4 (3 t + 4) > 2 (11 t + 11)$

Step 1.2

Simplify by adding zeros.

$4 (3 t + 4) > 2 (11 t + 11)$

Step 1.3

Apply the distributive property.

$4 (3 t) + 4 \cdot 4 > 2 (11 t + 11)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $3$ by $4$ .

$12 t + 4 \cdot 4 > 2 (11 t + 11)$

Step 1.4.2

Multiply $4$ by $4$ .

$12 t + 16 > 2 (11 t + 11)$

Step 2

Simplify $2 (11 t + 11)$ .

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Step 2.1

Apply the distributive property.

$12 t + 16 > 2 (11 t) + 2 \cdot 11$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $11$ by $2$ .

$12 t + 16 > 22 t + 2 \cdot 11$

Step 2.2.2

Multiply $2$ by $11$ .

$12 t + 16 > 22 t + 22$

Step 3

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

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Step 3.1

Subtract $22 t$ from both sides of the inequality.

$12 t + 16 - 22 t > 22$

Step 3.2

Subtract $22 t$ from $12 t$ .

$- 10 t + 16 > 22$

Step 4

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

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Step 4.1

Subtract $16$ from both sides of the inequality.

$- 10 t > 22 - 16$

Step 4.2

Subtract $16$ from $22$ .

$- 10 t > 6$

Step 5

Divide each term in $- 10 t > 6$ by $- 10$ and simplify.

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Step 5.1

Divide each term in $- 10 t > 6$ by $- 10$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 10 t}{- 10} < \frac{6}{- 10}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 10$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 10 t}{- 10} < \frac{6}{- 10}$

Step 5.2.1.2

Divide $t$ by $1$ .

$t < \frac{6}{- 10}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $6$ and $- 10$ .

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Step 5.3.1.1

Factor $2$ out of $6$ .

$t < \frac{2 (3)}{- 10}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $2$ out of $- 10$ .

$t < \frac{2 \cdot 3}{2 \cdot - 5}$

Step 5.3.1.2.2

Cancel the common factor.

$t < \frac{2 \cdot 3}{2 \cdot - 5}$

Step 5.3.1.2.3

Rewrite the expression.

$t < \frac{3}{- 5}$

Step 5.3.2

Move the negative in front of the fraction.

$t < - \frac{3}{5}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$t < - \frac{3}{5}$

Interval Notation:

$(- \infty, - \frac{3}{5})$