2.7.0: Linear Inequalities and Absolute Value Inequalities (Exercises)
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For the following exercises, solve the inequality. Write your final answer in interval notation.
60. 5x−8<12
61. −2x+5>x−7
62. x−13+x+25≤35
63. |3x+2|+1≤9
64. |5x−1|>14
65. |x−3|<−4
For the following exercises, solve the compound inequality. Write your answer in interval notation.
66. −4<3x+2≤18
67. 3y<1−2y<5+y
For the following exercises, graph as described.
68. Graph the absolute value function and graph the constant function. Observe the points of intersection and shade the x -axis representing the solution set to the inequality. Show your graph and write your final answer in interval notation. |x+3|≥5
69. Graph both straight lines (left-hand side being y−1 and right-hand side being y2) on the same axes. Find the point of intersection and solve the inequality by observing where it is true comparing the y -values of the lines. See the interval where the inequality is true. x+3<3x−4