Algebra Examples

$- 8 - 5 (10 t + 1) \geq 4 t - 10 - 9 t$

Step 1

Rewrite so $t$ is on the left side of the inequality.

$4 t - 10 - 9 t \leq - 8 - 5 (10 t + 1)$

Step 2

Subtract $9 t$ from $4 t$ .

$- 5 t - 10 \leq - 8 - 5 (10 t + 1)$

Step 3

Simplify $- 8 - 5 (10 t + 1)$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$- 5 t - 10 \leq - 8 - 5 (10 t) - 5 \cdot 1$

Step 3.1.2

Multiply $10$ by $- 5$ .

$- 5 t - 10 \leq - 8 - 50 t - 5 \cdot 1$

Step 3.1.3

Multiply $- 5$ by $1$ .

$- 5 t - 10 \leq - 8 - 50 t - 5$

Step 3.2

Subtract $5$ from $- 8$ .

$- 5 t - 10 \leq - 50 t - 13$

Step 4

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

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Step 4.1

Add $50 t$ to both sides of the inequality.

$- 5 t - 10 + 50 t \leq - 13$

Step 4.2

Add $- 5 t$ and $50 t$ .

$45 t - 10 \leq - 13$

Step 5

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

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Step 5.1

Add $10$ to both sides of the inequality.

$45 t \leq - 13 + 10$

Step 5.2

Add $- 13$ and $10$ .

$45 t \leq - 3$

Step 6

Divide each term in $45 t \leq - 3$ by $45$ and simplify.

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Step 6.1

Divide each term in $45 t \leq - 3$ by $45$ .

$\frac{45 t}{45} \leq \frac{- 3}{45}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $45$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{45 t}{45} \leq \frac{- 3}{45}$

Step 6.2.1.2

Divide $t$ by $1$ .

$t \leq \frac{- 3}{45}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Cancel the common factor of $- 3$ and $45$ .

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Step 6.3.1.1

Factor $3$ out of $- 3$ .

$t \leq \frac{3 (- 1)}{45}$

Step 6.3.1.2

Cancel the common factors.

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Step 6.3.1.2.1

Factor $3$ out of $45$ .

$t \leq \frac{3 \cdot - 1}{3 \cdot 15}$

Step 6.3.1.2.2

Cancel the common factor.

$t \leq \frac{3 \cdot - 1}{3 \cdot 15}$

Step 6.3.1.2.3

Rewrite the expression.

$t \leq \frac{- 1}{15}$

Step 6.3.2

Move the negative in front of the fraction.

$t \leq - \frac{1}{15}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$t \leq - \frac{1}{15}$

Interval Notation:

$(- \infty, - \frac{1}{15}]$