Linear Equations · Grade 7
How do you turn a sentence into an algebraic expression?
Choose a letter to stand for the number you do not know, then translate the sentence operation by operation: more is addition, times is multiplication, less is subtraction. An expression describes a quantity and has no equals sign; an equation claims two quantities are equal, and that is what can be solved.
Learning objectives
- Translate a verbal description into an algebraic expression with one variable
- Substitute a number for the variable and evaluate the expression
- Explain the difference between an algebraic expression and an equation
A letter is a number you do not know yet
Writing x is not writing something mysterious. It is writing a particular number that simply is not known to us yet, and it is treated exactly like any other number.
So you can add to it, multiply it, and substitute for it. Substituting is the fastest check that an expression was written correctly: put a number in, work it out, and see whether the result fits the story.
Translate word by word
More than and greater by are addition. Less than and smaller by are subtraction. Times and multiplied by are multiplication, and divided by is division. Most sentences translate in the order they were written.
Brackets are what gets missed. Five times the sum of x and two is not five x plus two — the brackets say to add first and multiply afterwards.
It is worth reading the expression back aloud after writing it. If the sentence that comes out is not the sentence you started with, something in the translation moved.
Expression or equation
An algebraic expression describes a quantity: x plus three. It has no equals sign and there is nothing to solve — you can only simplify it or substitute into it.
An equation claims two quantities are equal: x plus three equals seven. Now there is a claim that can be tested, and exactly one value of x satisfies it.
Worked examples
Write an expression: a number 7 greater than three times another number
- Choose a letter for the other number: call it x
- Three times that number: 3x
- Greater by 7 means adding 7
Answer: 3x plus 7
Write an expression: five times the sum of a number and two
- The sum of a number and two goes in brackets: (x + 2)
- Five times that whole sum
- The brackets mark that the addition comes first
Answer: 5(x + 2), which is not 5x plus 2
Find the value of 4x minus 3 when x is 5
- Substitute 5 for x: 4 times 5, minus 3
- Do the multiplication first: 20
- Subtract: 20 minus 3
Answer: 17
Common mistakes
- Skipping the brackets after the word times
- Five times the sum needs brackets, or the multiplication only reaches the first term. Substituting exposes it at once: at x equals one, one expression gives fifteen and the other seven.
- Trying to solve an expression
- An expression has no solution because it makes no claim. You can simplify it or substitute into it; solving needs an equals sign.
- Translating less than backwards
- A number three less than x is x minus three, not three minus x. Reading the sentence back aloud after writing it catches the reversal.
What to remember
- A letter is a number not yet known.
- Times is multiplication; greater by is addition.
- Brackets say what comes first.
- An expression describes; an equation claims.