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Unit 4: Expressions

What a letter standing in for a number buys you, and the two moves — distribute and combine — that simplify anything.

6 topics · 23 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 Is

  1. How it worksHow does covering an unknown number of marbles with a box let you write one equation for every possible amount inside?
  2. Common mistakeWhy does 3x mean 3 times x, and not just the digits 3 and x sitting next to each other?
  3. Common mistakeWhy doesn't the letter x always have to stand for the same number in every problem?
  4. Going furtherWhat happens to an expression when the same letter appears in it more than once?
Your turn1 of 2
In the expression 7x, what does putting the number 7 right next to the letter x mean?

Terms, Coefficients, and Constants

  1. How it worksHow do you identify the coefficient, the variable, and the constant term inside an expression like 4x plus 7?
  2. Worked exampleFind the coefficient, variable, and constant in the expression negative 3y plus 8.
  3. Common mistakeWhy isn't the constant term in an expression the same thing as its coefficient?
Your turn1 of 2
Priya earns 9 dollars for every hour, y, that she babysits, plus a flat 13 dollar bonus, written as 9y plus 13. What is the coefficient of y in that expression?

Writing Expressions from Words

  1. How it worksHow do you turn phrases like 'twice a number' or 'three less than a number' into symbols?
  2. Worked exampleShow me an expression for seven less than three times a number, and then for half of a number plus four.
  3. Common mistakeWhy doesn't 'five less than a number' translate to 5 minus x?
Your turn1 of 2
Write an expression for 7 less than 7 times a number n.

Evaluating Expressions

  1. How it worksHow do you substitute a value in for a variable and then work through the order of operations?
  2. Worked exampleFind the value of 3x plus 2y when x is 4 and y is negative 1.
  3. Worked exampleFind the value of 2 times the quantity n plus 5, when n is 7 dollars saved each week.
  4. Common mistakeWhy doesn't squaring a negative number you substitute in give you a negative result?
Your turn1 of 2
A robot's score formula is 7x plus 7y. Find the score when x is 8 and y is negative 3.

The Distributive Property

  1. How it worksHow does the distributive property turn a number times a group in parentheses into two separate multiplications?
  2. Worked exampleFind the simplified form of 5 times the quantity 2x minus 3.
  3. Common mistakeWhy doesn't distributing a negative number leave the sign inside the parentheses unchanged?
  4. Common mistakeWhy can't you cancel the x in the fraction x plus 3, all over x, down to just 3?
  5. Going furtherWhat happens when you distribute one expression into a set of parentheses that already has more than two terms inside?
Your turn1 of 2
Simplify -4 times the quantity 5x minus 8.

Combining Like Terms

  1. How it worksHow do matching variables and exponents tell you which terms in an expression are allowed to combine?
  2. Worked exampleFind the simplified form of 6x plus 4 minus 2x plus 9.
  3. Common mistakeWhy can't 4x and 4x squared be combined into a single term?
  4. Going furtherWhat happens when you combine like terms in an expression with three different variables mixed together?
Your turn1 of 2
Simplify 7x plus 6 minus 4x plus 3.