Grade 7 Algebra: Expressions, Equations & Variables (Pre-Algebra Foundation)

GRADE 7 MATHEMATICS • LESSON 6

Algebra

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Meet the letter that stands for a number. Learn terms, like terms and coefficients, collect and simplify expressions, substitute values, and expand brackets — then take 15 exams with full step-by-step solutions.

What is algebra?

Algebra is arithmetic with a letter standing in for a number we do not know yet. That letter is called a variable — often x or n.

So x + 3 means “some number, plus 3”. If x turns out to be 5, then x + 3 = 8. The power of algebra is writing a rule that works for every number at once.

Read it like this:   2x means “2 times the number”  •  x + 4 means “4 more than the number”  •  x − 1 means “1 less than the number”.

Words you must know

The exact vocabulary of an expression.

Variable
A letter that stands for a number, like x.
Term
A single part of an expression, separated by + or −. In 3x + 5, the terms are 3x and 5.
Coefficient
The number in front of the variable. In 3x, the coefficient is 3.
Constant
A plain number with no variable, like the 5 in 3x + 5.
Like terms
Terms with the same letter part, like 3x and 2x. Only like terms can be added together.
Expression
Letters and numbers joined by operations, like 3x + 5. It has no equals sign.
🧩 Like-Terms Collector

Build an expression and watch the x-terms and number terms get grouped and simplified.

Working with algebra

Your main study reference. Each skill is broken into numbered steps, each one explained, with a worked example and a teacher hack.

1) Collecting like terms (simplifying)

  1. Spot the like terms. Put the x-terms in one group and the plain numbers in another.
  2. Add each group. Add the coefficients of the x-terms; add the constants separately.
  3. Write the result. One x-term and one number, joined with + or −.
Example: 3x + 5 + 2x + 4
x-terms: 3x + 2x = 5x
numbers: 5 + 4 = 9
Answer: 5x + 9
Hack: you can only add terms that “match”. x and a plain number never combine — like apples and oranges.

2) Substituting a value

  1. Replace the letter. Put the given number wherever you see x.
  2. Follow order of operations. Multiply before you add or subtract.
  3. Work it out to a single number.
Example: find 3x + 5 when x = 4
3(4) + 5
= 12 + 5 = 17
Hack: always put the substituted number in brackets, like 3(4). It reminds you to multiply, not to write “34”.

3) Expanding brackets (the distributive law)

  1. The outside number multiplies everything inside. a(b + c) = a×b + a×c.
  2. Multiply the x-term. Outside number × the x-term.
  3. Multiply the constant. Outside number × the number inside.
Example: 3(2x + 4)
3 × 2x = 6x
3 × 4 = 12
Answer: 6x + 12
Hack: draw arrows from the outside number to each term inside so you never forget to multiply the second one.

4) Writing an expression from words

  1. Name the unknown. Let the mystery number be x.
  2. Translate each word. “times” means ×, “more than” means +, “less than” means −.
  3. Build the expression in the right order.
Example: “5 more than double a number”
double a number = 2x
5 more than that = 2x + 5
Hack: “less than” flips the order. “7 less than a number” is x − 7, not 7 − x.
🔢 Substitution Machine

Test Yourself — 15 Exams

Each exam has 10 questions, and every answer comes with a step-by-step solution — even when you get it right.

Key takeaways

1. A variable is a letter standing for a number. A coefficient is the number in front of it.

2. Only like terms combine: add the x-terms together and the numbers together.

3. To substitute, replace x with its value and multiply before adding.

4. To expand a(bx + c), multiply the outside number by every term inside.

5. “Less than” flips the order — “7 less than x” is x − 7.