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

$\begin{gathered} x\ge\frac{-4}{2} \\ x\ge-2 \end{gathered}$

Therefore, the solution is:

$x\ge-2$