Working With Algebra
Algebra is the heart of ACT Math. The goal is always to isolate the variable using inverse operations while keeping the equation balanced.
Linear Equations
Do the same thing to both sides. Solve 3x - 7 = 11: add 7 to get 3x = 18, then divide by 3 to get x = 6. Always check by substituting back: 3(6) - 7 = 11. Correct.
Distributing and Combining
Clear parentheses first: 2(x + 4) = 18 becomes 2x + 8 = 18, so 2x = 10 and x = 5.
Inequalities
Solve like equations, with one rule: flip the inequality sign when you multiply or divide by a negative number. Solve -2x < 6: divide by -2 and flip to get x > -3.
Systems of Equations
Two common methods:
- •Substitution: From y = 2x and x + y = 9, substitute to get x + 2x = 9, so x = 3 and y = 6.
- •Elimination: Add or subtract equations to cancel a variable. For x + y = 10 and x - y = 4, add them: 2x = 14, so x = 7 and y = 3.
Translating Words
Turn phrases into equations: "five less than twice a number" is 2n - 5. "A number is 8 more than another" is a = b + 8.
Key Takeaways
- •Isolate the variable with inverse operations, same on both sides.
- •Distribute before combining like terms.
- •Flip the inequality when multiplying or dividing by a negative.
- •Choose substitution or elimination, whichever cancels a variable fastest.
