Answer:
r > 5 1/4
Step-by-step 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 :)
