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Solve the System of Inequalities r/4<-5 or -2r-7<=3

User Jon W
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Final answer:

To solve the system, isolate r in each inequality: r/4 < -5 implies r < -20, and -2r - 7 <= 3 leads to r >= -5. The solution is r < -20 or r >= -5.

Step-by-step explanation:

To solve the system of inequalities r/4 < -5 or -2r - 7 ≤ 3, we first isolate r in each inequality.

For the first inequality:
r/4 < -5
Multiply both sides by 4 to get r < -20.

For the second inequality:
-2r - 7 ≤ 3
First, add 7 to both sides: -2r ≤ 10
Then, divide both sides by -2, remembering to reverse the inequality: r ≥ -5.

The solution to the system of inequalities is that r is either less than -20 or greater than or equal to -5.

User Corey
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