Question

Which of the following is not a way to represent the solution of the inequality 5(x + 2) greater than or equal to 7x + 2(x − 1)?
A number line with a closed circle on 3 and shading to the right.
A number line with a closed circle on 3 and shading to the left.
3 greater than or equal to x
x less than or greater to 3

Answer 1

Here is a step-by-step breakdown. Start at the top and read down the line, making sure you understand each step.
\[
\begin{align*}
5(x + 2) &\geq 7x + 2(x − 1) \quad\text{ distribute the 5 and the 2}\\
5x +10 &\geq 7x + 2x -2 \quad\text{ combine $7x$ and $2x$}\\
5x+10&\geq 9x -2 \quad\text{ move all constants to the left of the $\geq$ and all variables to the right}\\
10+2&\geq 9x-5x \quad\text{ combine variables and constants.}\\
12 &\geq 4x\quad\text{divide both sides by 4} \\
3 &\geq x
\end{align*}
\]

Answer 2

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