Question 91·Easy·Linear Inequalities in One or Two Variables

After you isolate the $x$ term, you will need to divide by a negative number. What happens to the inequality sign when you do that?

Once you have an inequality like $x<$ (or $x>$) some number, compare each answer choice to that number to see which ones could work.

In Desmos, type 5 - 2x > 9. Desmos will shade the region of $x$-values that satisfy this inequality along the $x$-axis.

Notice the vertical boundary line where the shading starts or ends; this corresponds to the value where $5-2x=9$. The shading will be on one side of this line, indicating all $x$-values that make the inequality true.

For each answer choice, type an expression like 5 - 2(-2) > 9, 5 - 2(1) > 9, etc. Desmos will show true or false next to each. The correct answer is the choice for which the inequality evaluates to true.

Start with the inequality $5-2x>9$.

Subtract 5 from both sides to move the constant term away from the $x$ term:

$5-2x-5>9-5$

This simplifies to

$-2x>4$.

Now you need to get $x$ by itself.

Divide both sides of $-2x>4$ by $-2$. When you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign:

$x< -2$.

So any value of $x$ that satisfies the inequality must be less than −2.

Check each answer choice against $x< -2$:

• $-2$ is not less than $-2$ (it is equal), so it does not work.
• $1$ and $7$ are greater than $-2$, so they do not work.
• $-3$ is less than $-2$, so it satisfies the inequality.

Therefore, the correct answer is $-3$.