Solve the Inequality for t 2-5(3t+10)>=5t+5+9

$2 - 5 (3 t + 10) \geq 5 t + 5 + 9$

Step 1

Simplify $2 - 5 (3 t + 10)$ .

Simplify each term.

Apply the distributive property.

$2 - 5 (3 t) - 5 \cdot 10 \geq 5 t + 5 + 9$

Multiply $3$ by $- 5$ .

$2 - 15 t - 5 \cdot 10 \geq 5 t + 5 + 9$

Multiply $- 5$ by $10$ .

$2 - 15 t - 50 \geq 5 t + 5 + 9$

Subtract $50$ from $2$ .

$- 15 t - 48 \geq 5 t + 5 + 9$

Step 2

Add $5$ and $9$ .

$- 15 t - 48 \geq 5 t + 14$

Step 3

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

Subtract $5 t$ from both sides of the inequality.

$- 15 t - 48 - 5 t \geq 14$

Subtract $5 t$ from $- 15 t$ .

$- 20 t - 48 \geq 14$

Step 4

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

Add $48$ to both sides of the inequality.

$- 20 t \geq 14 + 48$

Add $14$ and $48$ .

$- 20 t \geq 62$

Step 5

Divide each term in $- 20 t \geq 62$ by $- 20$ and simplify.

Divide each term in $- 20 t \geq 62$ by $- 20$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 20 t}{- 20} \leq \frac{62}{- 20}$

Simplify the left side.

Cancel the common factor of $- 20$ .

Cancel the common factor.

$\frac{- 20 t}{- 20} \leq \frac{62}{- 20}$

Divide $t$ by $1$ .

$t \leq \frac{62}{- 20}$

Simplify the right side.

Cancel the common factor of $62$ and $- 20$ .

Factor $2$ out of $62$ .

$t \leq \frac{2 (31)}{- 20}$

Cancel the common factors.

Factor $2$ out of $- 20$ .

$t \leq \frac{2 \cdot 31}{2 \cdot - 10}$

Cancel the common factor.

$t \leq \frac{2 \cdot 31}{2 \cdot - 10}$

Rewrite the expression.

$t \leq \frac{31}{- 10}$

Move the negative in front of the fraction.

$t \leq - \frac{31}{10}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$t \leq - \frac{31}{10}$

Interval Notation:

$(- \infty, - \frac{31}{10}]$

Solve the Inequality for t 2-5(3t+10)>=5t+5+9

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