Question

Solve the inequality 11x+4(x-2)<5x+2 and write the solution in interval notation

Answer 1

The inequality given is

`11x+4\mleft(x-2\mright)<5x+2`

Step 1: Expand the bracket

`\begin{gathered} 11x+4\mleft(x-2\mright)<5x+2 \\ 11x+4x-8<5x+2 \end{gathered}`

Step 2: collect similar terms

`\begin{gathered} 11x+4x-8<5x+2 \\ 15x-8<5x+2 \end{gathered}`

Step 3: Add 8 to both sides

`\begin{gathered} 15x-8<5x+2 \\ 15x-8+8<5x+2+8 \\ 15x<5x+10 \end{gathered}`

Step 4: Substract 5x from both sides

`\begin{gathered} 15x<5x+10 \\ 15x-5x<5x+10-5x \\ 10x<10 \end{gathered}`

Step 5: Divide both sides by 10

`\begin{gathered} (10x)/(10)<(10)/(10) \\ x<1 \end{gathered}`

Hence,

`\begin{bmatrix}\mathrm{Solution\colon}\: & \: x<1\: \\ \: \mathrm{Interval\: Notation\colon} & \: \mleft(-\infty\: ,\: 1\mright)\end{bmatrix}\text{ }`

Therefore,

The solution = x<1

The interval notattion = (-∞,1)