1. Equations & Inequalities

Solve each inequality. Give the solution set using interval notation.

$7x-2(x-3)\le 5(2-x)$

In Exercises 59–94, solve each absolute value inequality. 5 > |4 - x|

Solve each inequality. Give the solution set using interval notation.

$-8>3x-5>-12$

In Exercises 59–94, solve each absolute value inequality. 1 < |2 - 3x|

In Exercises 59–94, solve each absolute value inequality. $12 < \left| -2x + \frac{6}{7} \right| + \frac{3}{7}$

Solve each absolute value inequality. 4 + |3 - x/3| ≥ 9

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