Solve the Compound inequality.
5x - 7 < - 3 and 4x + 3 > - 1
To solve this compound inequality, we will solve each inequality separately and then find the intersection of the solutions.
1) 5x - 7 < - 3
Add 7 to both sides:
5x - 7 + 7 < - 3 + 7
5x < 4
Divide both sides by 5:
(5x)/5 < 4/5
x < 4/5
So the solution to the first inequality is x < 4/5.
2) 4x + 3 > - 1
Subtract 3 from both sides:
4x + 3 - 3 > - 1 - 3
4x > - 4
Divide both sides by 4:
(4x)/4 > (-4)/4
x > -1
So the solution to the second inequality is x > -1.
Therefore, the intersection of the solutions is the range where both inequalities are true, which is x < 4/5 and x > -1.