Solve the Inequality for t 6+4(-2t+9)>=t+2-7t

$6 + 4 (- 2 t + 9) \geq t + 2 - 7 t$

Step 1

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

$t + 2 - 7 t \leq 6 + 4 (- 2 t + 9)$

Step 2

Subtract $7 t$ from $t$ .

$- 6 t + 2 \leq 6 + 4 (- 2 t + 9)$

Step 3

Simplify $6 + 4 (- 2 t + 9)$ .

Simplify each term.

Apply the distributive property.

$- 6 t + 2 \leq 6 + 4 (- 2 t) + 4 \cdot 9$

Multiply $- 2$ by $4$ .

$- 6 t + 2 \leq 6 - 8 t + 4 \cdot 9$

Multiply $4$ by $9$ .

$- 6 t + 2 \leq 6 - 8 t + 36$

Add $6$ and $36$ .

$- 6 t + 2 \leq - 8 t + 42$

Step 4

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

Add $8 t$ to both sides of the inequality.

$- 6 t + 2 + 8 t \leq 42$

Add $- 6 t$ and $8 t$ .

$2 t + 2 \leq 42$

Step 5

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

Subtract $2$ from both sides of the inequality.

$2 t \leq 42 - 2$

Subtract $2$ from $42$ .

$2 t \leq 40$

Step 6

Divide each term in $2 t \leq 40$ by $2$ and simplify.

Divide each term in $2 t \leq 40$ by $2$ .

$\frac{2 t}{2} \leq \frac{40}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 t}{2} \leq \frac{40}{2}$

Divide $t$ by $1$ .

$t \leq \frac{40}{2}$

Simplify the right side.

Divide $40$ by $2$ .

$t \leq 20$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$t \leq 20$

Interval Notation:

$(- \infty, 20]$

Solve the Inequality for t 6+4(-2t+9)>=t+2-7t

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