Solved on Feb 20, 2024

Find the solution set for the inequality $\frac{-6 t}{7} \leq 72$ . Options: a) $t \leq-62$ , b) $t \geq-62$ , c) $t \leq-84$ , d) $t \geq-84$ .

STEP 1

Assumptions
1. We are given the inequality $\frac{-6 t}{7} \leq 72$ .
2. We need to solve for the variable $t$ .
3. The solution will be in the form of an inequality representing a set of values for $t$ .

STEP 2

To solve the inequality for $t$ , we first want to isolate $t$ on one side. We can start by multiplying both sides of the inequality by $7$ to eliminate the denominator.
$7 \times \frac{-6 t}{7} \leq 7 \times 72$

STEP 3

The $7$ on the left side cancels out the denominator, simplifying the inequality.
$-6t \leq 7 \times 72$

STEP 4

Now we can calculate the product on the right side of the inequality.
$-6t \leq 504$

STEP 5

Next, we want to isolate $t$ by dividing both sides of the inequality by $-6$ . Remember that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign.
$\frac{-6t}{-6} \geq \frac{504}{-6}$

STEP 6

Now we simplify both sides of the inequality.
$t \geq -84$

STEP 7

We have found the solution to the inequality. The solution set for the inequality $\frac{-6 t}{7} \leq 72$ is $t \geq -84$ .
The correct answer is d) $t \geq -84$ .

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Find the solution set for the inequality $\frac{-6 t}{7} \leq 72$ . Options: a) $t \leq-62$ , b) $t \geq-62$ , c) $t \leq-84$ , d) $t \geq-84$ .

STEP 1

Assumptions
1. We are given the inequality $\frac{-6 t}{7} \leq 72$ .
2. We need to solve for the variable $t$ .
3. The solution will be in the form of an inequality representing a set of values for $t$ .

STEP 2

To solve the inequality for $t$ , we first want to isolate $t$ on one side. We can start by multiplying both sides of the inequality by $7$ to eliminate the denominator.
$7 \times \frac{-6 t}{7} \leq 7 \times 72$

STEP 3

The $7$ on the left side cancels out the denominator, simplifying the inequality.
$-6t \leq 7 \times 72$

STEP 4

Now we can calculate the product on the right side of the inequality.
$-6t \leq 504$

STEP 5

Next, we want to isolate $t$ by dividing both sides of the inequality by $-6$ . Remember that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign.
$\frac{-6t}{-6} \geq \frac{504}{-6}$

STEP 6

Now we simplify both sides of the inequality.
$t \geq -84$

STEP 7

We have found the solution to the inequality. The solution set for the inequality $\frac{-6 t}{7} \leq 72$ is $t \geq -84$ .
The correct answer is d) $t \geq -84$ .

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Find the solution set for the inequality −6t7≤72\frac{-6 t}{7} \leq 727−6t​≤72. Options: a) t≤−62t \leq-62t≤−62, b) t≥−62t \geq-62t≥−62, c) t≤−84t \leq-84t≤−84, d) t≥−84t \geq-84t≥−84.

STEP 1

Assumptions1. We are given the inequality −6t7≤72\frac{-6 t}{7} \leq 727−6t​≤72.2. We need to solve for the variable ttt.3. The solution will be in the form of an inequality representing a set of values for ttt.

STEP 2

To solve the inequality for ttt, we first want to isolate ttt on one side. We can start by multiplying both sides of the inequality by 777 to eliminate the denominator.7×−6t7≤7×727 \times \frac{-6 t}{7} \leq 7 \times 727×7−6t​≤7×72

STEP 3

The 777 on the left side cancels out the denominator, simplifying the inequality.−6t≤7×72-6t \leq 7 \times 72−6t≤7×72

STEP 4

Now we can calculate the product on the right side of the inequality.−6t≤504-6t \leq 504−6t≤504

STEP 5

Next, we want to isolate ttt by dividing both sides of the inequality by −6-6−6. Remember that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign.−6t−6≥504−6\frac{-6t}{-6} \geq \frac{504}{-6}−6−6t​≥−6504​

STEP 6

Now we simplify both sides of the inequality.t≥−84t \geq -84t≥−84

STEP 7

We have found the solution to the inequality. The solution set for the inequality −6t7≤72\frac{-6 t}{7} \leq 727−6t​≤72 is t≥−84t \geq -84t≥−84.The correct answer is d) t≥−84t \geq -84t≥−84.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the solution set for the inequality $\frac{-6 t}{7} \leq 72$ . Options: a) $t \leq-62$ , b) $t \geq-62$ , c) $t \leq-84$ , d) $t \geq-84$ .

Assumptions
1. We are given the inequality $\frac{-6 t}{7} \leq 72$ .
2. We need to solve for the variable $t$ .
3. The solution will be in the form of an inequality representing a set of values for $t$ .

To solve the inequality for $t$ , we first want to isolate $t$ on one side. We can start by multiplying both sides of the inequality by $7$ to eliminate the denominator.
$7 \times \frac{-6 t}{7} \leq 7 \times 72$

The $7$ on the left side cancels out the denominator, simplifying the inequality.
$-6t \leq 7 \times 72$

Now we can calculate the product on the right side of the inequality.
$-6t \leq 504$

Next, we want to isolate $t$ by dividing both sides of the inequality by $-6$ . Remember that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign.
$\frac{-6t}{-6} \geq \frac{504}{-6}$

Now we simplify both sides of the inequality.
$t \geq -84$

We have found the solution to the inequality. The solution set for the inequality $\frac{-6 t}{7} \leq 72$ is $t \geq -84$ .
The correct answer is d) $t \geq -84$ .