Question

Work each problem according to the instructions given.a. Solve: 3x - 5 = 0b. Solve: |3x - 5| = 0c. Solve: 3x - 5 = 1d. Solve: |3x - 5| = 1

Answer 1

We will find x for the given equations:

a) 3x - 5 = 0

so, the solution will be as follows:

`\begin{gathered} 3x-5=0 \\ 3x=5 \\ x=(5)/(3) \end{gathered}`

b) |3x-5| = 0

It is an absolute function equation and

it will give the same solution as part (a)

So,

`x=(5)/(3)`

c) 3x - 5 = 1

the solution will be as follows:

`\begin{gathered} 3x-5=1 \\ 3x=1+5 \\ 3x=6 \\ x=(6)/(3)=2 \end{gathered}`

d) |3x - 5| = 1

So, writing the equation according to the absolute value rule

`\begin{gathered} 3x-5=\pm1 \\ \text{when,}3x-5=1\rightarrow3x=6\rightarrow x=(6)/(3)=2 \\ \text{when,}3x-5=-1\rightarrow3x=4\rightarrow x=(4)/(3) \end{gathered}`

so, the answer will be x = 2, 4/3