One & Two Step EquationsINTEGRATED MATHEMATICS
Vocabulary• Equation: A statement that the values of two mathematical expressions are equal• Inverse Operations: Operations that undo one another
1) Separate the Equation
2) ISOLATE THE VARIABLE:• Should It Stay or Should It Go (Variables on
Left/Constants on Right)
Solving a One-Step Equation
Examples:
Property of EqualityYou 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.4) z – 7 = 4Ex.3) 19 = y + 7
One-Step Equations with Addition/Subtraction
Try These:
1) x + 4 = 10 2) y - 2 = 12
3) 15 = 23 + r
4) -13 + z = 2
Property of EqualityYou 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) = 5 Ex.8) = 4
The two negatives will cancel each other out.
The two fives will cancel each other out.
What Do We Do with Negative Fractions?
Recall that
Solve .
Multiply both sides by -5.
−𝑥5=−𝑥5
=𝑥−5
−𝑥5
=3
One-Step Equations with Multiplication/Division
Try These:
1) 25 = 5x
2) -4x = -12
3) = 4
4) - = 24
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 EquationsEx.9) Solve 5x + 7 = 3
Ex.10) Solve + 15 = 45
Two-Step Equations
Ex.12) Solve 11z + 8 = 30
Ex.11) Solve 4 = -6y - 20
Two-Step EquationsEx.13) Solve 4 = -11 +
Ex.14) Solve 20 – c = -9
Two-Step EquationsTry These:1) 11x + 2 = 352) 8 = - 22 + 2b3) 2 = 5x – 8
4) -32 = 4t - 165) – 7 = –4
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