Solve the Inequality for t -2t-3(10t+5)>=3t-9-6t

$- 2 t - 3 (10 t + 5) \geq 3 t - 9 - 6 t$

Step 1

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

Simplify each term.

Apply the distributive property.

$- 2 t - 3 (10 t) - 3 \cdot 5 \geq 3 t - 9 - 6 t$

Multiply $10$ by $- 3$ .

$- 2 t - 30 t - 3 \cdot 5 \geq 3 t - 9 - 6 t$

Multiply $- 3$ by $5$ .

$- 2 t - 30 t - 15 \geq 3 t - 9 - 6 t$

Subtract $30 t$ from $- 2 t$ .

$- 32 t - 15 \geq 3 t - 9 - 6 t$

Step 2

Subtract $6 t$ from $3 t$ .

$- 32 t - 15 \geq - 3 t - 9$

Step 3

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

Add $3 t$ to both sides of the inequality.

$- 32 t - 15 + 3 t \geq - 9$

Add $- 32 t$ and $3 t$ .

$- 29 t - 15 \geq - 9$

Step 4

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

Add $15$ to both sides of the inequality.

$- 29 t \geq - 9 + 15$

Add $- 9$ and $15$ .

$- 29 t \geq 6$

Step 5

Divide each term in $- 29 t \geq 6$ by $- 29$ and simplify.

Divide each term in $- 29 t \geq 6$ by $- 29$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 29 t}{- 29} \leq \frac{6}{- 29}$

Simplify the left side.

Cancel the common factor of $- 29$ .

Cancel the common factor.

$\frac{- 29 t}{- 29} \leq \frac{6}{- 29}$

Divide $t$ by $1$ .

$t \leq \frac{6}{- 29}$

Simplify the right side.

Move the negative in front of the fraction.

$t \leq - \frac{6}{29}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$t \leq - \frac{6}{29}$

Interval Notation:

$(- \infty, - \frac{6}{29}]$

Solve the Inequality for t -2t-3(10t+5)>=3t-9-6t

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