How can I turn a sentence about an unknown number into an equation?

First, decide exactly what the unknown is and give it a name. For example, let x be the number. Then identify the relationship the sentence describes, rather than trying to turn each word into a symbol by itself. A useful sequence is: name the unknown, restate the relationship, translate it into an equation, and check the result against the original wording. [S1]

An equation has two expressions joined by an equals sign, so the sentence needs to describe what is equal to what. [S2] For example, in “A number plus 8 is 20,” x represents the number, and “is 20” tells you the left-hand expression equals 20:

x + 8 = 20

Read it aloud: “the number plus 8 equals 20.” That matches the sentence.

Build the expression in the order the relationship describes. Let x be the number. “Twice a number” is 2x; “three more than” that amount is 2x + 3; and “is 11” makes it equal to 11. So the equation is:

2x + 3 = 11

You can check the translation without solving: read its left side as “three more than twice x,” then its right side as “11.” It matches the original sentence. If you do solve it, subtract 3 from both sides to get 2x = 8, then divide by 2 to get x = 4. Check the number in the original wording: twice 4 is 8, and three more is 11.

The check matters because a familiar word is not a complete translation rule. The relationship in the whole sentence—not a keyword alone—determines the equation. [S1]

Name both quantities and write what is being taken away from what. For instance: “Seven less than a number is 12.” Let x be the number. Seven less than that number means x − 7, so the equation is:

x − 7 = 12

Read the left side as “seven less than x.” It should not say “x less than seven”; that would reverse the quantities and give a different expression.

Compare a different sentence: “Seven minus a number is 12.” Here the starting amount is 7 and the number is subtracted from it, so write 7 − x = 12. Reading each expression back in words helps catch an order mix-up before solving. These are examples of translating complete sentences, not a universal dictionary in which one word always triggers one symbol. [S2]

Try this short template:

1. Unknown: Let x = [the quantity the sentence asks about].
2. Relationship in words: Restate how the quantities relate.
3. Expression: Translate each quantity and operation in that relationship.
4. Equation: Use = where the sentence says the two sides are equal.
5. Read back: Say the equation in words and compare it with the original sentence.
6. If solving: Check your answer in the original sentence.

Worked example: “Five times a number, decreased by 2, is 18.” Let x be the number. Five times the number is 5x; decreased by 2 gives 5x − 2; “is 18” gives 5x − 2 = 18. Solving gives x = 4, and checking gives five times 4, decreased by 2, equals 18.

The method helps organize the translation, but wording can still be ambiguous. If you cannot confidently restate the relationship, pause and clarify what the sentence means before writing an equation. [S1][S2]