Math  /  Algebra

Question召.7. Which of the following are solutions to the inequality below? Select all that appl m31\frac{m}{3} \geq 1 m=126m=126 m=96m=96 m=60m=60 m=69m=69

Studdy Solution

STEP 1

What is this asking? Which of these values of mm make m3\frac{m}{3} greater than or equal to 1? Watch out! Don't forget to perform the same operation on both sides of the inequality to isolate mm.

STEP 2

1. Isolate *m*
2. Check each value

STEP 3

We have the inequality m31\frac{m}{3} \geq 1.
Our goal is to get mm all by itself!
It's currently being divided by **3**.
To isolate mm, we need to undo this division.
How do we undo division by **3**?
We multiply by **3**!

STEP 4

Remember, whatever we do to one side of the inequality, we *must* do to the other side to keep things balanced.
So, let's multiply both sides of the inequality by **3**: m3313 \frac{m}{3} \cdot 3 \geq 1 \cdot 3

STEP 5

On the left side, the **3** in the numerator and the **3** in the denominator divide to one, leaving just mm.
Awesome! On the right side, 13=31 \cdot 3 = 3.
So, our inequality becomes: m3 m \geq 3 This tells us that mm must be greater than or equal to **3**.

STEP 6

Is 126126 greater than or equal to **3**?
Yes! So, m=126m = 126 is a solution.

STEP 7

Is 9696 greater than or equal to **3**?
Absolutely! So, m=96m = 96 is a solution.

STEP 8

Is 6060 greater than or equal to **3**?
You bet!
So, m=60m = 60 is a solution.

STEP 9

Is 6969 greater than or equal to **3**?
For sure!
So, m=69m = 69 is a solution.

STEP 10

All the given values (m=126m = 126, m=96m = 96, m=60m = 60, and m=69m = 69) are solutions to the inequality!

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