Intermediate Algebra Problems With Answers -
Sample 9 - Solve Absolute Value Equations

Several algebra problems, related to solving equations with absolute value, are presented along with their answers. The solutions are at the bottom of the page. These questions may be used with the tutorials on how to Solve Equations with Absolute Value.

Solve the following absolute value equations.
a) | x | = 5
b) | x - 2 | = 7
c) | 89 x + 4 | = -2
d) | -11 x - 9 | = 0
e) 2 | x + 5 | = 10
f) 3 | -9 x - 7 | - 2 = 13
g) -5 | -x + 2 | + 8 = -12
h) | -3 x - 2 | / 3 = 7
i) | (x - 5) / 4 | = 6
j) | x + 1 | = |- 4 x + 3|
k) | x + 3 | = - |- x - 3 |

Answers to the Above Questions
a) {-5 , 5}
b) {-5 , 9}
c) No solutions (absolute value is not negative)
d) {-9/11}
e) {0 , -10}
f) given equation is equivalent to | -9 x - 7 | = 5 , solutions: {-4/3 , -2/9}
g) given equation is equivalent to | -x + 2 | = 4 , solutions: {-2 , 6}
h) given equation is equivalent to | -3 x - 2 | = 21 , solutions: {-23/3 , 19/3}
i) given equation is equivalent to | x - 5 | = 24, solutions: {-19 , 29}
j) {1/6 , 1}
k) given equation is equivalent to 2| x + 3 | = 0 , solution: {-3}

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