Question

Solve the inequality: (1 + 7x > 7 - 9x), express the solution in terms of intervals, and illustrate the solution set on the real number line.

a) (x < -0.25) or (x > 0.5)

b) (x < -0.5) or (x > 0.25)

c) (x < -0.75) or (x > 0.75)

d) (x < -0.2) or (x > 0.2)

Answer 1

The inequality (1 + 7x > 7 - 9x) simplifies to x > 0.375. The solution in interval notation is (x > 0.375) and is represented on the number line with a shading to the right of the point 0.375.

Step-by-step explanation:

To solve the inequality (1 + 7x > 7 - 9x), we need to isolate the variable x. We will begin by adding 9x to both sides of the inequality and simultaneously subtracting 1 from both sides to collect like terms on one side. This yields the following steps:

1. 1 + 7x + 9x > 7 - 9x + 9x
2. 1 + 16x > 7 (Simplified left side by combining like terms)
3. 16x > 7 - 1 (Subtracted 1 from both sides)
4. 16x > 6
5. x > 0.375 (Divided both sides by 16)

The solution to the inequality expressed in interval notation is (x > 0.375). When plotting this solution on the real number line, the area to the right of the point 0.375 is shaded, indicating all the values of x that satisfy the inequality.