Question

What is the greatest whole number value that makes the inequality $4x+4\le 12$ true?

Answer 1

Hint: We try to take points which have x coordinates that satisfies $4x+4\le 12$. There is no restriction on the y coordinates. Based on the points we try to find the space or region in the 2-D plane which satisfies $4x+4\le 12$. We take all the constants together and divide that by 4.

Complete step by step answer:
The inequation $4x+4\le 12$ represents the space or region in the 2-D plane where the x coordinates of points satisfy $4x+4\le 12$. We can solve the inequalities by treating them as equations for the operations like addition and subtraction. In case of multiplication and division we need to watch out for the negative values as that changes the inequality sign.We take all the constants on one side.
$4x\le 12-4 \\
\Rightarrow 4x\le 8 $
Now we divide with 4 and get
\[\dfrac{4x}{4}\le \dfrac{8}{4} \\
\therefore x\le 2 \]

Therefore, the greatest whole number value that makes the inequality $4x+4\le 12$ true is 2.

Note: We can also express the inequality as the interval system where $4x+4\le 12$ defines that $x\in \left( -\infty ,2 \right]$. The interval for the y coordinates will be anything which can be defined as $y\in \left( -\infty ,\infty \right)$. We also need to remember that the points on the line $4x+4\le 12$ will not be the solution for the inequation.