← Algebra I

Unit 1: Algebra Foundations

What a variable actually stands for, the order operations must happen in, and the two moves that make every later unit possible.

5 topics · 21 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

What a Variable Actually Represents

  1. How it worksHow does a variable let you write one equation that works for every possible value at once?
  2. Worked exampleFind the value of the expression 5x - 3 when x is 4.
  3. Common mistakeWhy isn't x always secretly standing for the number 1?
  4. Going furtherWhat happens to an expression's value when you swap in a negative number for its variable?
Your turn1 of 2
Find the value of the expression 7x - 6 when x is 9.

Order of Operations

  1. How it worksHow does the order of operations decide which move happens first in a mixed expression?
  2. Worked exampleFind the value of 8 minus 2 times the quantity 3 plus 1, using the correct order of operations.
  3. Common mistakeWhy doesn't order of operations mean you always work strictly left to right?
  4. Going furtherWhat changes about the order of operations once parentheses are nested inside other parentheses?
Your turn1 of 2
Find the value of 24 minus 4 times the quantity 6 plus 2.

Evaluating Algebraic Expressions

  1. How it worksHow do you substitute a value into an expression without breaking the order of operations?
  2. Worked exampleFind the value of 2a2 - 3b when a is 3 and b is 5.
  3. Common mistakeWhy doesn't squaring a negative number plugged into x2 give you a negative result?
  4. Worked exampleFind the value of -x2 + 4 when x is -2.
Your turn1 of 2
Find the value of 5a2 - 4b when a is 6 and b is 3.

Combining Like Terms

  1. How it worksHow do matching variables and exponents tell you which terms are allowed to combine?
  2. Worked exampleFind the simplified form of 4x + 7 - 2x + 3.
  3. Common mistakeWhy can't 3x and 3x2 be combined into one term?
  4. Going furtherWhat happens when you combine like terms across more than two groups of parentheses?
Your turn1 of 2
Simplify 8x + 6 - 4x + 3.

The Distributive Property

  1. How it worksHow does the distributive property turn 3 times the quantity x plus 4 into 3x plus 12?
  2. Worked exampleFind the simplified form of -2 times the quantity 3x minus 5.
  3. Common mistakeWhy isn't the expression x plus 3, divided by 3, the same as just x?
  4. Common mistakeWhy doesn't distributing a minus sign leave the second term's sign unchanged?
  5. Going furtherWhat happens when you distribute one set of parentheses into another set of parentheses right next to it?
Your turn1 of 2
Simplify -3 times the quantity 5x minus 8.