Solve and graph the compound inequality on a number line x/4 < -1 and x + 7 > -2 Select the correct answer from the following

a) x > -6
b) All real numbers
c) -6 < x < 6
d) - 8 < x < -4
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1 answer

To solve the compound inequality:
x/4 < -1 and x + 7 > -2

Let's solve each inequality separately and then find the intersection of their solutions.

1) x/4 < -1
Multiply both sides of the inequality by 4 (since 4 is positive and we don't need to flip the inequality sign):

x < -4

2) x + 7 > -2
Subtract 7 from both sides of the inequality:

x > -9

Now let's find the intersection of these two solutions. We want values of x that satisfy both inequalities.

The solutions to the compound inequality are x < -4 and x > -9.

Graphically on a number line:

--------------(-9)======(-4)-----------------

The shaded area represents the values of x that satisfy both inequalities.

The correct answer is d) -8 < x < -4.