HiSET Math: Algebraic Concepts

What you need to know

Algebra questions test translating words into expressions, simplifying expressions, solving linear equations and inequalities, working with formulas, graphing lines, and interpreting slope and intercepts. You should be able to solve a two-step equation, isolate any variable in a formula, and read a linear pattern from a table or description.

Traps to watch for

• Inequalities: multiplying or dividing by a negative number flips the inequality sign. Adding or subtracting never does.
• Distributing negatives: −(x − 3) becomes −x + 3, not −x − 3.
• Slope: slope is change in y over change in x, so keep the order consistent in numerator and denominator.
• Word problems: define the variable explicitly. "Five less than twice a number" is 2x − 5, not 5 − 2x.
• Checking: substitute your solution back into the original equation. This catches sign errors almost every time.

Rule of thumb

Whatever you do to one side of an equation, do to the other. Undo operations in reverse order: addition/subtraction first, then multiplication/division.

Worked example

Solve 3(x − 2) = 4x + 5. Distribute: 3x − 6 = 4x + 5. Subtract 3x: −6 = x + 5. Subtract 5: x = −11. Check: 3(−13) = −39 and 4(−11) + 5 = −39. Both sides match.