Question

What is the solution set for |s - 4| = 6?

1) s = -2 and s = 2
2) s = -10 and s = 2
3) s = -10 and s = 10
4) s = 2 and s = 10

Answer 1

The correct solution set for the equation |s - 4| = 6 is option 3) s = -10 and s = 10.

Step-by-step explanation:

The given equation |s - 4| = 6 can be split into two cases:
`\( s - 4 = 6 \) and \( -(s - 4) = 6 \).`

For the first case, solving
`\( s - 4 = 6 \) gives \( s = 10 \).`

For the second case, solving
`\( -(s - 4) = 6 \) gives \( s = -10 \).`

So, the solution set includes both
`\( s = -10 \) and \( s = 10 \),` making option 3) the correct answer. This is because the absolute value function yields two possible solutions for the given equation. It's essential to consider both the positive and negative cases when dealing with absolute value equations. In this context, the values
`\( s = -10 \) and \( s = 10 \)`satisfy the original equation.
`\( |s - 4| = 6 \). Therefore, the solution set is \( s = -10 \) and \( s = 10 \).`