1. Equations & Inequalities

In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions. $y_1 = \frac{x}{2} + 3, \quad y_2 = \frac{x}{3} + \frac{5}{2}, \quad \text{and} \quad y_1 \leq y_2$

Use interval notation to represent all values of x satisfying the given conditions. y₁ = (2/3)(6x - 9) + 4, y₂ = 5x + 1, and y₁ > y₂

Use interval notation to represent all values of x satisfying the given conditions. y = 2x - 11 + 3(x + 2) and y is at most 0

Use the method described in Exercises 83–86, if applicable, and properties of absolute value to solve each equation or inequality. (Hint: Exercises 99 and 100 can be solved by inspection.)

Use interval notation to represent all values of x satisfying the given conditions. y = |2x - 5| + 1 and y > 9

Solve and graph the solution set on a number line: 3|2x-1| ≥ 21

Use interval notation to represent all values of x satisfying the given conditions. y = 8 - |5x + 3| and y is at least 6

Use the graph of y = |4 - x| to solve each inequality.

|4 - x| ≥ 5

Use the table to solve each inequality. - 3 < 2x - 5 ≤ 3

When 3 times a number is subtracted from 4, the absolute value of the difference is at least 5. Use interval notation to express the set of all numbers that satisfy this condition.

When 4 times a number is subtracted from 5, the absolute value of the difference is at most 13. Use interval notation to express the set of all numbers that satisfy this condition.

Solve and graph the solution set on a number line: (2x−3)/4 ≥ 3x/4 + 1/2

Solve each equation or inequality.

$\mid 8-5x\mid \ge 2$

Solve each equation or inequality.

$\mid 7x-3\mid >4$

Solve each equation or inequality.

$\mid 7x+8\mid -6>-3$