Question 410·Easy·Algebra

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Which of the following values of $t$ satisfies the inequality $5 - 3t > 11$ ?

A linear inequality compares an expression containing a variable with a fixed value. Graph the condition in Desmos to see which side of a boundary works; a strict sign like $>$ leaves the boundary out. If you solve by hand, watch the negative coefficient: dividing an inequality by a negative reverses its sign.

Hints

Hint 1
Desmos uses $x$ for horizontal values. Replace $t$ with $x$ but keep the greater-than sign. Which side of the boundary does Desmos shade?
Hint 2
A strict inequality such as $>$ doesn't include equality. A value on the dashed boundary won't work; look for a listed value inside the shading.

Step-by-step

Approach 1: Graph the allowed values
Step 1
Find the shaded side
Type $5-3x>11$ in Desmos. Replacing $t$ with $x$ changes only the variable's name, so the graph shows the values the question allows. Desmos shades to the left of $x=-2$ . Its dashed boundary means $-2$ itself is excluded.
Step 2
Check the listed values
Type the choices as points, using each value for the first coordinate and $0$ for the second. Desmos shows only $(-5,0)$ inside the shading; $(-2,0)$ sits on the excluded boundary. So $t=-5$ satisfies the inequality. Choice D.

Approach 2: Solve by hand to see the sign flip
Step 1
Remove the constant
Subtract $5$ from both sides of the inequality. Subtraction keeps the greater-than sign pointing the same way:
$-3t>6$
Step 2
Get $t$ alone
Divide both sides by $-3$ . A negative reverses the order of numbers, so flip $>$ to $<$ :
$t<-2$
Step 3
Choose a value in the range
The sign $<$ means $t$ must be less than $-2$ . Of the listed values, only $-5$ is below $-2$ , so it satisfies the inequality. Choice D.

Lessons that teach this

SAT AlgebraIntermediateCoreSolve one-variable inequalities

Question 410·Easy·Algebra

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