To solve for a, we need to consider two cases: when -4a + 10 is positive and when -4a + 10 is negative. Case 1: -4a + 10 is positive -4a + 10 > 0 -4a > -10 a 0 4a - 10 > 0 4a > 10 a > 10/4 a > 2.5 Therefore, the solution for the equation ∣−4a+10∣ = 42 is a > 2.5 or a < 2.5. In interval notation, the solution is (-∞, 2.5) U (2.5, ∞).

42=

∣−4a+10∣

1 answer

To solve for a, we need to consider two cases: when -4a + 10 is positive and when -4a + 10 is negative.

Case 1: -4a + 10 is positive
-4a + 10 > 0
-4a > -10
a < 10/4
a < 2.5

Case 2: -4a + 10 is negative
-(-4a + 10) > 0
4a - 10 > 0
4a > 10
a > 10/4
a > 2.5

Therefore, the solution for the equation ∣−4a+10∣ = 42 is a > 2.5 or a < 2.5. In interval notation, the solution is (-∞, 2.5) U (2.5, ∞).