Algebraic Thinking
What this domain covers
Algebraic Thinking asks you to translate words into expressions and equations, evaluate expressions for given values, combine like terms, apply the distributive property, and solve one- and two-step linear equations and inequalities. You also need to read function tables, recognize patterns, work with the coordinate plane, interpret slope as a rate of change, and connect a linear equation in y = mx + b form to its graph.
Solving equations safely
Whatever you do to one side, do to the other. Undo addition and subtraction before multiplication and division, and clear parentheses first. Check your answer by substituting it back into the original equation - many errors surface instantly.
Traps to watch for
- Distributing a negative: −3(x − 4) becomes −3x + 12, not −3x − 12.
- Reversing the inequality symbol when you multiply or divide both sides by a negative number.
- Word-order reversal: five less than a number is x − 5, not 5 − x.
- Subtracting terms that are not alike, such as 3x and 5.
- Reading slope with the wrong sign, or confusing slope with the y-intercept.
Worked example
Solve 5 − 2(x − 3) = 17. Distribute: 5 − 2x + 6 = 17. Combine: 11 − 2x = 17. Subtract 11: −2x = 6. Divide by −2: x = −3. Check: 5 − 2(−6) = 5 + 12 = 17. Rule of thumb: isolate the variable by peeling operations off in reverse order, and verify every solution.