One & Two Step Equations Integrated Mathematics

Vocabulary Equation: A statement that the values of two mathematical expressions are equal Inverse Operations: Operations that undo one another

Solving a One-Step Equation 1) Separate the Equation 2) ISOLATE THE VARIABLE: Should It Stay or Should It Go (Variables on Left/Constants on Right) Examples: 𝒙=𝟕 𝒚=𝟕𝟐

Property of Equality You can add or subtract any number to BOTH sides of an equation and the equation will still hold true.

One-Step Equations with Addition/Subtraction Ex.1) x + 2 = 6 Ex.2) a – 4 = 2

One-Step Equations with Addition/Subtraction Ex.3) 19 = y + 7 Ex.4) z – 7 = 4

One-Step Equations with Addition/Subtraction Try These: 2) y - 2 = 12 1) x + 4 = 10 3) 15 = 23 + r 4) -13 + z = 2

Property of Equality You can multiply or divide BOTH sides of an equation by any number and the equation will still hold true.

An Easy Example: (don’t copy) We all know that 3 = 3. Does 3(4) = 3? NO! But 3(4) = 3(4). The equation is still true if we multiply both sides by 4. Would you ever put deodorant under just one arm? Would you ever put nail polish on just one hand? Would you ever wear just one sock?

One-Step Equations with Multiplication/Division Ex.5) -2x = 8 Ex.6) 3y = 15

One-Step Equations with Multiplication/Division Ex.7) 𝑧 3 = 5 Ex.8) 𝑦 4 = 4

What Do We Do with Negative Fractions? Recall that The two negatives will cancel each other out. The two fives will cancel each other out. − 𝑥 5 = −𝑥 5 = 𝑥 −5 −𝑥 5 =3 Solve . Multiply both sides by -5.

One-Step Equations with Multiplication/Division Try These: 3) 𝑥 5 = 4 1) 25 = 5x 4) - 𝑧 2 = 24 2) -4x = -12

Two-Step Equations 1) Separate the Equation 2) Should It Stay or Should It Go Addition/Subtraction Multiplication/Division 3) Solve for Variable

Two-Step Equations Ex.9) Solve 5x + 7 = 3

Two-Step Equations Ex.10) Solve 𝑡 3 + 15 = 45

Two-Step Equations Ex.11) Solve 4 = -6y - 20

Two-Step Equations Ex.12) Solve 11z + 8 = 30

Two-Step Equations Ex.13) Solve 4 = -11 + 𝑝 −5

Two-Step Equations Ex.14) Solve 20 – 1 7 c = -9

Two-Step Equations Ex.15) Solve 2𝑥−3 3 =5

Two-Step Equations 1) 11x + 2 = 35 4) -32 = 4t - 16 2) 8 = -22 + 2b Try These: 1) 11x + 2 = 35 4) -32 = 4t - 16 2) 8 = -22 + 2b 5) 𝟒𝒏 𝟓 – 7 = –4 6) 3𝑥+4 2 =5 3) 2 = 5x – 8

Write Linear Equations - ADDITION The SUM of a number and 4 5 MORE than a number 2 PLUS 7 13 ADDED TO a number A number INCREASED by 9 The SUM of two numbers

Write Linear Equations - Subtraction 3 LESS THAN a number A number DECREASED BY 15 7 MINUS a number A number Subtracted from 6 The DIFFERENCE BETWEEN two numbers

Write Linear Equations - Multiplication The PRODUCT of two numbers 8 TIMES a number A number MULTIPLIED BY 9 TWICE a number 𝟑 𝟒 𝑶𝑭 a number The PRODUCT of two numbers

Write Linear Equations - Division The QUOTIENT of 6 and a number A number DIVIDED by 4 The RATIO of 7 and a number