In the inequality , which of the following values of satisfies the inequality?

Solution available with step-by-step explanation

SAT Linear Inequalities Question 91 | Free SAT Prep | Aniko

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

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In the inequality $5-2x>9$ , which of the following values of $x$ satisfies the inequality?

For one-variable linear inequalities, treat them almost like equations: first isolate the term with $x$ by adding or subtracting on both sides, then solve for $x$ by dividing by the coefficient. Always remember that multiplying or dividing both sides by a negative number flips the inequality sign. Once you have a solution like $x<k$ or $x>k$ , quickly compare each answer choice to that condition (or plug choices back into the original inequality) to see which one actually makes the statement true.

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First simplify the inequality

Try moving the constant term (the number without $x$ ) to the other side of the inequality so that the $x$ term is alone on one side.

Be careful with negative coefficients

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?

Use your solution to check the choices

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

Desmos Guide

Graph the inequality

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

Locate the boundary point

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.

Test each answer choice

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.

Step-by-step Explanation

Isolate the term with x

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

$-2x>4$ .

Solve for x and remember the inequality rule

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.

Compare the solution to the answer choices

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 $-3$ .

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Desmos Guide

Step-by-step Explanation

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Desmos Guide

Step-by-step Explanation