Of course, I'd be happy to help you with the expression \(3|x-1|+5\).
This expression involves the absolute value of \((x-1)\), which means it could have two different forms depending on whether \((x-1)\) is positive or negative.
1. When \(x-1\) is **positive** or zero, \(|x-1|\) is equal to \(x-1\). So, for \(x-1 \geq 0\), the expression simplifies to:
\[3(x-1) + 5\]
2. When \(x-1\) is **negative**, \(|x-1|\) is equal to \(-(x-1)\). So, for \(x-1 < 0\), the expression simplifies to:
\[3(-(x-1)) + 5\]
Let's simplify both cases:
1. For \(x-1 \geq 0\):
\[3(x-1) + 5 = 3x - 3 + 5 = 3x + 2\]
2. For \(x-1 < 0\):
\[3(-(x-1)) + 5 = -3(x-1) + 5 = -3x + 3 + 5 = -3x + 8\]
So, the expression \(3|x-1|+5\) can be simplified to:
- \(3x + 2\) when \(x \geq 1\)
- \(-3x + 8\) when \(x < 1\)
Depending on the value of \(x\ and whether it is greater than or less than 1, you can use one of these simplified forms.