Solving One-Step One-Variable Equations

Solving One-Step Equations

Feel free to write these on paper! I will put notes in your OneNote notebook after class.

Vocabulary

• Variable = unknown value represented with a letter (x, y, etc.)

• Isolate = get something by itself (alone)

• Inverse operations = opposite math operations

• Multiplication & Division are Inverses

• Addition & Subtraction are Inverses

• Property of Equality = solve by doing the same operation on BOTH sides of the equation.

Multiple Choice

How would you solve this equation?

$$2x\ =\ 6$$  

• Add 2 on both sides

• Subtract 2 on both sides

• Multiply by 2 on both sides

• Divide by 2 on both sides

Multiple Choice

How would you solve this equation?

x - 5 = 10

• Divide 5 on both sides

• Add 5 on both sides

• Subtract 5 on both sides

• Multiply 5 on both sides

Multiple Choice

How would you solve this equation?

$$\frac{x}{3}=7$$  

• Add 3 on both sides

• Multiply by 3 on both sides

• Subtract 3 on both sides

• Divide by 3 on both sides

Multiple Choice

How would you solve this equation?

$$x\ +\ 9\ =\ 11$$  

• Subtract 9 on both sides

• Add 9 on both sides

• Multiply by 9 on both sides

• Divide by 9 on both sides

Multiple Choice

How would you solve this equation?

$$\frac{3}{4}x\ =\ 6$$  

• Subtract 3/4 on both sides

• Multiply by 4/3 on both sides

• Add 4/3 to both sides

Reciprocals

A fraction flipped is called a reciprocal! When you multiply a fraction by its reciprocal, it equals 1! ("It cancels out")

Ex:

 $\frac{1}{3}\left(\frac{3}{1}\right)\ =\ 1$  

 $\frac{4}{5}\times\frac{5}{4}=1$  

Multiple Choice

How would you solve this equation?

$$-3x\ =\ 12$$  

• Add 3 on both sides

• Multiply by -3 on both sides

• Divide by -3 on both sides

• Subtract 3 on both sides

Multiple Choice

Solve for y.

$$\frac{y}{3}\ =\ 12$$  

• y = 36

• y = -36

• y = 4

• y = -4

Multiple Choice

Solve the equation:

4p = 16

• p = 12

• p = -12

• p = -4

• p = 4

Multiple Choice

Solve the equation:

-4 + r = 10

• r = 14

• r = 6

• r = -6

• r = 40

Multiple Choice

What is the first step to solve this equation:

3x = 44

• Add 3 to both sides

• Subtract 3 from both sides

• Multiply 3 on both sides

• Divide 3 on both sides.

Multiple Choice

How would you solve this equation: 9x=153?

• multiply

• divide

• add

• subtract

Multiple Choice

Solve for x.

x + 12 = 20

• x = 32

• x = -32

• x = 8

• x = -8

Multiple Choice

Solve the equation:

-5x = 25

• x = 20

• x = -20

• x = -5

• x = 5

Multiple Choice

x - 62 = 123

How should you show your work to isolate the variable and solve the equation?

• Add 62 to each side.

• Subtract 62 from each side.

• Multiply each side by 62.

• Add 123 to each side.

Multiple Choice

Solve for x:

• x = 20

• x = 7

• x = 10

• x = 3

Multiple Choice

Solve for b.

6b = 30

• b = 36

• b = 24

• b = 180

• b = 5

The end!

Time for Imagine Math/Catch up time :)