What this skill covers
This category spans solving for an unknown in linear equations up through evaluating functions and setting up equations that model a described situation.
When a word problem describes a situation with a fixed starting amount plus a rate (a membership fee plus a per-visit charge, for example), translating it into y = mx + b form first makes the rest of the question mechanical.
Worked examples
Example 1
If 5x − 3 = 2x + 9, what is the value of x?
A. 4
B. 3
C. 6
D. 2
Why: Subtract 2x from both sides: 3x − 3 = 9. Add 3: 3x = 12. Divide by 3: x = 4.
Example 2
A gym charges a $20 signup fee plus $15 per month. Which expression gives the total cost after m months?
A. 20 + 15m
B. 15 + 20m
C. 20m + 15m
D. 35m
Why: The fixed fee ($20) is added once, and the monthly rate ($15) is multiplied by the number of months — matching the standard fixed-cost-plus-rate structure.
How to practice this on TSI Practice Prep
Open ACT Practice to answer original ACT questions on aCT Algebra and Functions, get an explanation for every choice, and see this skill tracked separately in your progress and mistake review.
Practice score estimates are learning indicators, not official scores or admission guarantees.
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