Question

Mar 21, 5:36:03PM Solve for all values of a in simplest form. 42=|-4a+10|

Answer 1

The values of a that satisfy the equation 42 = |-4a + 10| are -8 and 13 after considering the equation with the absolute value expression set to both its positive and negative values.

Step-by-step explanation:

To solve for all values of a in the expression 42 = |-4a + 10|, we need to consider both the positive and negative scenarios of the absolute value.

First scenario (positive case):

1. 42 = -4a + 10
2. 42 - 10 = -4a
3. 32 = -4a
4. a = -8

Second scenario (negative case):

1. 42 = -(-4a + 10)
2. 42 = 4a - 10
3. 42 + 10 = 4a
4. 52 = 4a
5. a = 13

Thus, the values of a that satisfy the equation in simplest form are -8 and 13.