Question

Solve 2r ≤ 3(2r - 7)

Answer 1

you have:
2r
`\leq`6r-21
then move the 6r over to the left and you end up wtih
-4r
`\leq`-21
Then you divide by -4 and when you do you must flip the inequality so your answer would be
r
`\geq`21/4

Answer 2

r > 5 1/4

Explanation:

In algebra, the goal is always to isolate the variable so that its value can be determined. Since this is an inequality, there will still not be a specific value, but a set of values that will satisfy the variable.

Step 1: Use Distributive Property

2r < 6r - 21

Step 2: Subtract 6r

-4r < -21

Step 3: Divide by -4

Note: We must reverse the inequality sign, since we have divided by a negative number.

r > 5 1/4

Step 4: Check

2(5 1/4) < 3(2(5 1/4) - 7)

10 1/2 < 3(10 1/2) - 7

10 1/2 < 24 1/2✔ 24 1/2 is greater than 10 1/2, so this is correct.

Step 5: Double Check

Since this is an inequality, many values can satisfy it, let's try another one, just to make sure we are correct. We'll use 7 this time, since it is higher than 5 1/4.

2(7) < 3(2(7) - 7)

14 < 3(14) - 7

14 < 35✔

Step 6: Answer

r > 5 1/4 or 21/4

I'm always happy to help :)