High School

Solve the inequalities:

[tex]-6x + 14 < -28[/tex] or [tex]9x + 15 \leq -12[/tex]

Choose the correct option:

A. [tex]x > 7[/tex]
B. [tex]x < 7[/tex]
C. [tex]x > -7[/tex]
D. [tex]x < -7[/tex]

Answer :

Final answer:

To solve the compound inequality [-6x + 14 < -28 or 9x + 15 ≤ -12], we solve each inequality individually. The first inequality gives us x > 7, and the second gives us x ≤ -3. Since it's an 'or' statement and both solutions don't overlap, the answer is x > 7.

Explanation:

To solve the compound inequality [-6x + 14 < -28 or 9x + 15 ≤ -12], we need to split it into two separate inequalities and solve each one individually.

First, let's solve -6x + 14 < -28:

  • Add -14 to both sides: -6x < -42
  • Divide by -6, remembering to reverse the inequality: x > 7

Now, let's solve 9x + 15 ≤ -12:

  • Subtract 15 from both sides: 9x ≤ -27
  • Divide by 9: x ≤ -3

Since we are dealing with an 'or' statement, we take the union of both solutions.

The first inequality gives us x > 7, which is not satisfied by any values that satisfy the second inequality x ≤ -3.

Therefore, the correct answer is (a) ( x > 7 ) because this is the only solution that cannot overlap with the solution to the second inequality.