Variables, Expressions, and Equations

ACT Math · Axiom Academy

LESSON Variables, Expressions, and Equations What a variable is, how to evaluate and translate expressions, and how to solve for one — the toolkit every later algebra topic on the ACT builds from 1. What a Variable Is — and Evaluating an Expression A variable (usually x , y , or n ) is a placeholder for a number that can change or isn't known yet. To evaluate an expression means to substitute a specific number in for the variable, then simplify using order of operations. Watch 2 flow into x below. A second worked example — negative substitution Evaluate x^2-4x+1 when x=-3 . Substitute carefully (keep the negative in parentheses): (-3)^2-4(-3)+1 . Then simplify left to right: . 2. Translating Words Into Algebra One of the most important ACT skills is turning an English phrase into a mathematical expression — it's the gateway to every word problem. Watch the phrase below assemble into its expression, piece by piece. 1. "Sarah is 5 years older than John. If John is j years old, write an expression for Sarah's age." Older means addition, so Sarah's age is j+5 . 2. "A store sells notebooks for n dollars each. Write an expression for the cost of 12 notebooks." Twelve notebooks at n dollars each costs 12n dollars. Like terms have the same variable raised to the same power — only like terms can be combined. Watch matching terms below slide together and merge into one. Simplify 3x+5x : both terms have x , so combine directly: 3x+5x=8x .

This is the written version of the interactive lesson above. See the full ACT Math course.