Question

Solve l1 - 4x > 7

Option 1: x < -1.5 U x > 1.5
Option 2: x < -1.5 U x > 2
Option 3: x < -1.5
Option 4: x < 1.5 U x > 2

Answer 1

The correct solution to the inequality l1 - 4x > 7 is x < -1.5 OR x > 2 which corresponds to Option 2: x . To solve, we created two separate inequalities and found the solution for each, then combined them.

Step-by-step explanation:

We need to solve the inequality l1 - 4x > 7. To do this, we start by isolating the term containing x:

• Absolute values can be split into two inequalities. The equation inside the absolute value can be greater than 7 or less than -7 (since absolute value represents distance from zero).
• So, we can write two inequalities: 1 - 4x > 7 and 1 - 4x < -7.
• For the first inequality: 1 - 4x > 7. Subtracting 1 from both sides gives -4x > 6, and dividing both sides by -4 (remembering to flip the inequality sign) gives x < -1.5.
• For the second inequality: 1 - 4x < -7. Subtracting 1 from both sides gives -4x < -8, and dividing by -4 gives x > 2.
• Combining both solutions gives us the final answer: x < -1.5 OR x > 2.

The correct option is Option 2: x < -1.5 U x > 2.