More on Inequalities and Problem Solving

Example 1: Solve 2/3 x – 1/2 x > ¾

Example 2: Solve

Example 3: Solve

Example 4: Solve x ≥ 1.6 + 0.2x

Example 5: Solve 0.08x + 0.09(x + 100) ≥ 43

Example 6: Graph the solution set for the conjunction x > - 1 and x < 3

Example 7: Solve the conjunction 3x + 1 > - 5 and 2x + 5 > 7, and graph its solution set on a number line.

Example 8: Graph the solution set for the disjunction x < -1 or x > 2, and express it using interval notation

Example 9: Solve the disjunction 2x – 5 < -11 or 5x + 1 ≥ 6, and graph its solution set on a number line.

Example 10: Sari had scores of 94, 84, 86 and 88 on her first four exams of the semester. What score must she obtain on the fifth exam to have an average of 90 or better for the five exams?

Example 11: An investor has $1000 to invest. Suppose she invests $500 at 8% interest. At what rate must she invest the other $500 so that the two investments together yield more than $100 of yearly interest?

Example 12: If the temperature for a 24-hour period ranged between 41⁰F and 59⁰F, inclusive (that is 41 ≤ F ≤  59), what was the range in Celsius degrees?