Question

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

Let x be the unknown number. Then, the statement "8 increased by three times a number" can be written as

`8+3x`

and the statement "it is a least 4 more than the number" can be written as

`\ge4+x`

By combining these result, the inequality is:

`8+3x\ge4+x`

Now, let's solve for x.

By subtracting x to both sides of the last inequality, we get

`8+2x\ge4`

and by subtracting 8 to both sides, we have

`2x\ge-4`

By dividing both sides by 2, we obtain

`\begin{gathered} x\ge(-4)/(2) \\ x\ge-2 \end{gathered}`

Therefore, the solution is:

`x\ge-2`