Question 97·Easy·Linear Inequalities in One or Two Variables
What is the solution set of the inequality ?
For one-variable linear inequalities, treat them almost exactly like linear equations: first collect all x-terms on one side and constants on the other by using the same operation on both sides, then divide by the coefficient of x. Always pause before the last step to check the sign of the number you are dividing by; only flip the inequality when you divide or multiply by a negative. Finally, match the resulting inequality form (for example, x less than a number or x greater than a number) to the choices and, if unsure, quickly test a sample value from your solution set in the original inequality.
Hints
Get all x-terms together
Start by moving all the x-terms to one side of the inequality. What can you add or subtract from both sides to remove from the right side?
Isolate the x-term
Once you have an expression like on one side, how can you use addition or subtraction to get rid of the constant term next to ?
Handle the coefficient of x
After isolating , divide both sides by the coefficient of . Think about whether dividing by this number will change the direction of the inequality sign.
Desmos Guide
Enter the inequality
In Desmos, type 5x - 8 < 2x + 7 exactly as shown. Desmos will show a number line or shaded region representing all x-values that satisfy the inequality.
Read the solution from Desmos
Look at the solution statement that appears above the graph or number line (it will look like x with an inequality symbol and a number). Note the boundary value and whether the inequality symbol points toward smaller or larger numbers, then choose the matching answer choice.
Step-by-step Explanation
Collect x-terms on one side
Start with the inequality:
Subtract from both sides to get all x-terms on the left:
which simplifies to
Move constant terms to the other side
Now add 8 to both sides to isolate the x-term:
so
Solve for x and match the answer choice
Divide both sides by 3. Since 3 is positive, the inequality sign stays the same:
so
This matches answer choice B, .