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