Question

mp you be the teacher your friend solves the inequality and graphs the solution. is your friend correct? explain your reasoning. 27. $x - 7 > -2$ \\(\

$$\begin{align*}\\underline{+7} \\quad \\underline{+7}\\\\x > 5\\end{align*}$$

\\) number line with 3,4,5,6,7,8, filled dot at 5, line to right 28. $8 \leq x + 3$ \\(\

$$\begin{align*}\\underline{-3} \\quad \\underline{-3}\\\\5 \\leq x\\end{align*}$$

\\) number line with 3,4,5,6,7,8, filled dot at 5, line to left section 4.5 solving inequalities using addition or subtraction

Explanation:

Step1: Analyze problem 27 solution

The inequality is $x - 7 > -2$. Adding 7 to both sides gives $x > 5$, which is algebraically correct. But the graph uses a closed dot at 5, which is for $\leq$ or $\geq$. For $x > 5$, an open dot is needed.

Step2: Analyze problem 28 solution

The inequality is $8 \leq x + 3$. Subtract 3 from both sides: $8 - 3 \leq x$, so $5 \leq x$ (or $x \geq 5$), which is algebraically correct. However, the graph points left from 5, which represents values less than or equal to 5. For $x \geq 5$, the graph should point right with a closed dot at 5.

Answer:

1. For problem 27: Your friend is not correct. The algebraic solution $x > 5$ is right, but the graph uses a closed dot at 5 instead of an open dot (open dots are used for strict inequalities like $>$).
2. For problem 28: Your friend is not correct. The algebraic solution $5 \leq x$ is right, but the graph is drawn in the wrong direction; it should extend to the right from 5 (to represent values greater than or equal to 5) instead of to the left.