Answer:
Explanation:
o solve the compound inequality, we'll start by solving each inequality separately, and then find the intersection of their solutions.
For the first inequality: 8r - 3 ≥ 7r - 7
Adding 7r to both sides: 8r - 3 + 7r ≥ 7r - 7 + 7r
Combining like terms: 15r - 3 ≥ 14r
Subtracting 14r from both sides: 15r - 14r - 3 ≥ 0
Combining like terms: r - 3 ≥ 0
Adding 3 to both sides: r ≥ 3
For the second inequality: 2r + 4 ≤ r - 3
Subtracting 2r from both sides: 2r + 4 - 2r ≤ r - 3 - 2r
Combining like terms: 4 ≤ -r - 3
Adding r and 3 to both sides: 4 + r + 3 ≤ -r
Combining like terms: 7 ≤ -r
Multiplying both sides by -1: r ≤ -7
The solution to the compound inequality is the intersection of the solutions to each inequality, which is the range of r that satisfies both conditions. So, the solution is 3 ≤ r ≤ -7.
To graph the solution, we can plot the two inequalities on the number line, and shade the region between 3 and -7: