Question

7) 8 increased by three times a number is at least 4 more than the number. Write and solve an inequalityto determine the solution.

Answer 1

7) 8 increased by a number is written as 8+y

three times a number is: 3x

4 more than the number is: 4+x

Thus, the expression is

`8+3x\ge4+x`

Solving for x,

`\begin{gathered} \Rightarrow8+3x-x\ge4+x-x \\ \Rightarrow8+2x\ge4 \\ \Rightarrow-8+8+2x\ge-8+4 \\ \Rightarrow2x\ge-4 \\ \Rightarrow x\ge-(4)/(2)=-2 \\ \Rightarrow x\ge-2 \end{gathered}`

The answer is x>=-2