Write algebraic expressions and equations that model a verbal situation (translating words into math, not solving).
Free, timed SHSAT practice sets on translating words to expressions— every question includes a full worked explanation, and there's no account required.
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Translate one phrase at a time. Use a letter such as \(x\) for "a number".
Watch the order with "less than" and "subtracted from". "9 less than a number" starts with the number: \(x - 9\), not \(9 - x\). "7 less than 5 times a number" is \(5x - 7\).
"Times the sum" needs parentheses. "2 times the sum of a number and 9" is \(2(x + 9)\). Without parentheses, \(2x + 9\) multiplies only the \(x\).
For a word problem, multiply the rate by the number of units and add a one-time fee only once. A phone plan with a \(30\)-dollar fee plus \(25\) dollars a month costs \(c = 25m + 30\) after \(m\) months.
"20 less than a number" means start with the number and take 20 away: \(x - 20\). (Writing the parts in the order you read them gives \(20 - x\), which subtracts in the wrong order. \(x + 20\) adds instead of subtracting. \(20 < x\) is an inequality, not an expression: "less than" here means subtract.)
"The sum of a number and 6" must be grouped first: \((x + 6)\). Then multiply by 5: \(5(x + 6)\). (Leaving out the parentheses, \(5x + 6\), multiplies only the \(x\) by 5. \(x + 30\) multiplies only the 6 by 5. Writing \(5 + x + 6\) adds the 5 instead of multiplying by it.)
The \(15\)-dollar monthly charge is multiplied by the number of months \(m\), and the single \(20\)-dollar fee is added once: \(c = 15m + 20\). (\(c = 20m + 15\) charges the one-time fee every month. \(c = 35m\) adds the fee into the monthly rate. \(c = 15m - 20\) takes the fee away instead of adding it.)