To solve the compound inequality x/4 < -1 and x + 6 > -2, we will solve each inequality separately and then find the intersection of the solutions.
For the first inequality, we have x/4 < -1. To isolate x, we can multiply both sides by 4 (remembering to flip the inequality sign since we are multiplying by a negative number):
x/4 < -1
4*(x/4) > 4*(-1)
x > -4
So the solution to the first inequality is x > -4.
For the second inequality, we have x + 6 > -2. To isolate x, we can subtract 6 from both sides:
x + 6 > -2
x + 6 - 6 > -2 - 6
x > -8
So the solution to the second inequality is x > -8.
To find the intersection of the solutions, we look for values that satisfy both inequalities. Since x must be greater than -4 and also greater than -8, the solution is x > -4.
Now, let's graph this solution on a number line:
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2
|---|---|---|---|---|---|---|---|---|---|
x > -4
The shaded area shows the solution to the compound inequality x/4 < -1 and x + 6 > -2, which is x > -4.
Solve and graph the compound inequality on a number line.
x/4 < -1 and x + 6 > -2
1 answer