Algebra: Expressions, Equations, and Systems
What this domain tests
Algebra questions probe your ability to manipulate expressions and solve equations and inequalities. You need solid skills in expanding and factoring polynomials, including difference of squares $a^2-b^2=(a-b)(a+b)$ and simple trinomial factoring. You should solve linear equations, quadratic equations (by factoring, completing the square, or the quadratic formula), and systems of two equations in two variables. Understand slope-intercept and standard forms of a line, and how to interpret the discriminant $b^2-4ac$ to count real solutions. Also expect work with rational expressions and the rules for solving inequalities, including when the inequality sign flips.
Traps to watch for
A frequent error is forgetting to reverse the inequality when multiplying or dividing by a negative number. When solving rational equations, check for extraneous solutions that make a denominator zero. With systems, be careful that a question asking for the value of an expression like $x+y$ may be solved faster by adding the equations than by full substitution. Distribute negatives carefully: $-(x-3)=-x+3$, not $-x-3$. When factoring, always look first for a greatest common factor.
Worked example
Solve $2(x-3)+4 = 3x - 5$. Expand: $2x-6+4 = 3x-5$, so $2x-2 = 3x-5$. Subtract $2x$ from both sides: $-2 = x-5$. Add $5$: $x = 3$. Check by substitution: left side $= 2(0)+4 = 4$; right side $= 9-5 = 4$. Both sides match. Rule of thumb: isolate the variable step by step and always substitute your answer back into the original equation to catch sign errors.