Question

Answer 1

a) \(A=\left|x-5\right|+2x-3\)

\(=\left[{}\begin{matrix}x-5+2x-3\left(x\ge5\right)\\5-x+2x-3\left(x< 5\right)\end{matrix}\right.\)

\(=\left[{}\begin{matrix}3x-8\left(x\ge5\right)\\x+2\left(x< 5\right)\end{matrix}\right.\)

b) \(B=5x-4+\left|x+2\right|\)

\(=\left[{}\begin{matrix}5x-4+x+2\left(x\ge-2\right)\\5x-4-x-2\left(x< -2\right)\end{matrix}\right.\)

\(=\left[{}\begin{matrix}6x-2\left(x\ge-2\right)\\4x-6\left(x< -2\right)\end{matrix}\right.\)