Question

Determine the solutions of the equation: absolute value of the quantity one fourth times x plus 7 end quantity minus 3 equals 24?

1) x = -136 and x = 136
2) x = -136 and x = 80
3) x = -112 and x = 80
4) x = -80 and x = 80

Answer 1

The solutions to the equation |(1/4)x + 7| - 3 = 24 are x = 80 and x = -136. We solve this by isolating the absolute value expression and considering both the positive and negative scenarios.

Step-by-step explanation:

The student asked to determine the solutions for the equation: |(1/4)x + 7| - 3 = 24. To solve for x, we first isolate the absolute value expression by adding 3 to both sides of the equation: |(1/4)x + 7| = 27. Next, we consider two cases due to the absolute value:

1. (1/4)x + 7 = 27
2. -(1/4)x - 7 = 27

For the first case, we subtract 7 from both sides and then multiply by 4 to get x = 80. For the second case, we subtract 7 from both sides, which gives -(1/4)x = 34, and after multiplying by -4, we find x = -136. Therefore, the two possible solutions are x = 80 and x = -136.