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Expressions and Equations

Learn about variables, coefficients, expressions, equations, and inequalities. Understand how to write and solve equations with detailed examples and explanations.

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Expressions and Equations

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  1. Expressions and Equations

  2. Vocabulary • Variable - a letter that is used to represent an unknown number • Coefficient - A constant (number) that is in front of a variable (Ex: 4 is the coefficient in 4x) • Expression - A collection of constants, variables, and operations - NO EQUAL SIGN (Ex: 3x + 2)

  3. Vocabulary continued • Term - The individual parts of an expression (Ex: 4x and 2 in 4x+2) • Equation - shows that two or more expressions are equal (Ex: 4x - 2 = 6) • Inequality - shows that two or more expressions are NOT equal by using >, <, ≤, or ≥ (Ex: 2x + 1 > 5)

  4. Writing Expressions • Phrases can be turned into algebraic expressions by looking for clue words • Ex: the total of 5 and c will be written as 5 + c • Ex: the product of k and 9 will be written 9k (when being multiplied the number always comes before the variable)

  5. Clue words • Addition: add, sum, plus, more than, total, all together • Subtraction: minus, take away, less, less than, difference, decrease • Multiplication: times, product, twice • Division: quotient, divided into, divided by, out of

  6. Writing Equations • Equations are different from expressions because they contain an equal sign • Ex: A number increased by 7 is 11 would be written: x + 7 = 11

  7. Writing Equations • Break the sentence into parts to turn it into an algebraic equation: Ex: Four less than three times a number is fourteen Four less than means - 4 Three times a number means 3n Is fourteen means =14 So 3n - 4 = 14

  8. Solving equations • Equations must stay balanced. • To solve an equation, you must get the variable alone on one side of the equal sign. To do this, you must get rid of any other numbers by performing the opposite function. BUT whatever you do to one side, you must do to the other.

  9. Solving Equations • X + 3 = 6 • We need to get x by itself so we get rid of 3 by subtracting (opposite of addition) - BUT what we do to one side we must do to the other • X + 3 - 3 = 6 - 3 • This leaves x = 3

  10. Solving Equations • Ex: n - 7 = 3 • We want the n by itself so we have to get rid of the 7 so we add (opposite of subtraction) 7 BUT what we do to one side we must do to the other • N - 7 + 7 = 3 + 7 • N = 10

  11. Solving equations • EX: 3n = 12 • We want n by itself so we must get rid of the 3. 3n means 3 times n so we have to do the opposite function - divide. BUT what we do to one side, we must do to the other • 3n ÷ 3 = 12 ÷ 3 • N = 4

  12. Solving equations • Ex: n ⁄ 4 = 5 • We have to get n by itself. N and 4 are divided so we do the opposite - multiply BUT what we do to one side we must do to the other. • N ⁄ 4 x 4 = 5 x 4 • N = 20

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