High School

We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

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.

Thanks for taking the time to read 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. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada