Linear Equations Introduction Flashcards

Grade 7 · Math · Flashcards

Master the vocabulary, properties, and steps for solving one- and two-step linear equations.

Flashcards

Linear equation: An equation with variables raised only to the first power; has a straight-line graph
Solution to an equation: The value of the variable that makes both sides of the equation equal
Inverse operations: Pairs of operations that undo each other: + and −, × and ÷
Properties of Equality: Performing the same operation on both sides keeps an equation balanced
Isolate the variable: Use inverse operations to get the variable alone on one side of the equation
Solving a one-step equation: Apply one inverse operation to both sides. Example: x + 6 = 10 → subtract 6 → x = 4
Solving a two-step equation: Step 1: undo addition/subtraction. Step 2: undo multiplication/division. Example: 3x - 4 = 11 → +4 → 3x = 15 → ÷3 → x = 5
Checking a solution: Substitute the answer for the variable in the original equation and verify both sides are equal
Translating words to equations: Increased by = +, decreased by = −, times = ×, quotient of = ÷, is/equals = =
Negative coefficient: When the coefficient of x is negative, divide both sides by a negative number, which flips the sign of x. Example: -4x = 20 → x = -5
Coefficient: The number multiplied by the variable in a term; in 5x the coefficient is 5
Constant: A number in an equation with no variable attached; in 3x + 7 = 13, both 7 and 13 are constants