Question

Solve the compound inequality (2x - 1 > 3) or (4x - 5 > -13) or write the solution in interval notation. If there is no solution, enter ( emptyset ).

a) ( x < -1 ) or ( x > 2 )
b) ( x > -1 ) or ( x < 2 )
c) ( x < -2 ) or ( x > 1 )
d) ( x > -2 ) or ( x < 1 )

Answer 1

The solution to the compound inequality (2x - 1 > 3) or (4x - 5 > -13) is (x > -2) or (x > 2), represented in interval notation as (-2, ∞).

Step-by-step explanation:

To solve the compound inequality (2x - 1 > 3) or (4x - 5 > -13), we need to solve each inequality separately.

For the first inequality, 2x - 1 > 3:

• Add 1 to both sides: 2x > 4.
• Divide both sides by 2: x > 2.

For the second inequality, 4x - 5 > -13:

• Add 5 to both sides: 4x > -8.
• Divide both sides by 4: x > -2.

The solution to the compound inequality is finding the union of the solutions for each part, which in this case is any number greater than -2 or greater than 2. The correct answer is (x > -2) or (x > 2), which means that x can be any number that is greater than -2, including numbers that are also greater than 2.

The solution in interval notation is (-2, ∞).