RTI Variables on One Side

Multi-Step Equations with Variables on One Side

Open Ended

What steps should you always complete first with multi-step equations in order to have a 2-step equation left?

DCI

Steps:

1. Distribute, if necessary

2. Combine like terms, if necessary

3. Inverse operations are used to solve for the variable

Solve for x:

13x -9x + 20 = 30 + 2

Multiple Choice

13x -9x + 20 = 30 + 2

What should you do first?

• distribute

• combine like terms

• inverse operation

Multiple Select

13x -9x + 20 = 30 + 2

Check all terms which are like terms

• 13x and -9x

• 13x and 20

• 30 and 2

Like terms have the same variable with the same exponent

- 13x and -9x both have an x with the same exponent of 1 so they are like terms

- 30 and 2 are both constants with no variable so they are like terms

Fill in the Blanks

What does the equation simplify to when you combine the like terms on both the left and right side of the equation?

13x -9x + 20 = 30 + 2

Do not use spaces in the answer.

Multiple Choice

What is the next step in solving 4x + 20 = 32?

• Add 20

• Subtract 20

• Multiply by 4

• Divide by 4

When using inverse operations, you must work backwards and undo that which was last done to the variable.

The last thing was adding 20 so its opposite (subtracting 20) will undo that addition

Multiple Choice

What is the next step to solve 4x = 12?

• Divide by 4

• Subtract 4

• Multiply by 4

The answer is x=3

Since x was multiplied by 4 it is necessary to use its opposite, division, to undo that

Solve for x:

4(x - 3) = 20

Multiple Choice

What is the first step to solving 4(x - 3) = 20?

• inverse operations

• Combine like terms

• distribute

Distribute is first in DCI.

Multiple Choice

What is the correct order of inverse operations for solving 4x - 12 = 20?

• first subtract 12 and then divide by 4

• first add 12 and then subtract 4

• first add 12 and then divide by 4

Subtracting 12 was the last thing done to x so we must first add 12 to undo the subtraction. Next, we divide to undo the multiplication

Solve for x:

3x + 2(2x - 1) = 33

Multiple Choice

3x + 2(2x - 1) = 33

What is the first step?

• combine like terms

• distribute

• inverse operations

Distribution comes first in DCI

Fill in the Blanks

Next we combine like terms. Simplify 3x + 4x - 2 = 33

Do not use spaces

Multiple Choice

To finish, solve 7x - 2 = 33 using inverse operations

• x=5

• x=28

• x=-5

• x=-28

Multiple Choice

The objective when solving an equation is to....

• isolate the variable.

• check the solution.

• guess and check.

• Combine Like Terms.

Multiple Select

Which of the following are basic rules used for solving algebraic equations?

• Whatever you do to one side of the equal sign, you must copy and do on the other side of the equal sign

• Negative signs can be ignored

• Always start on the left side, regardless of where the variable is

• Always do the opposite operation

Multiple Choice

What is the first step in solving this equation?

• add 4 to both sides

• distribute the 4

• subtract 4 to both sides

• subtract 12 to both sides

Multiple Choice

What will the equation look like after you distribute?

• -6x - 8 = 10

• -6x + 8 = 10

• -5x - 6 = 10

• -5x + 6 = 10

Multiple Choice

What is the first step in the equation:

2x - 3 + 4x = 27

• Combine Like Terms

• Add 3 on both sides

• Divide by 2 on both sides

• Subtract 4x from both sides

Multiple Choice

Solve the following equation!

$$3x\ +\ 4=-11$$  

• x = 7/3

• x = -5

• x = 5

• x = -7/3

Fill in the Blanks

Solve the following equation:

$2\left(x+4\right)=14$  

Multiple Choice

Solve. $$6a\ +\ 5a\ =\ -11$$  

• $$a\ =\ 0$$  

• $$a\ =\ 1$$  

• $$a\ =\ -1$$  

• None of these

Multiple Choice

$$21=3+4n+5n$$  

• 9

• $$-7$$  

• 6

• 2

Multiple Choice

$$96=6\left(k+8\right)$$  

• $$12$$  

• $$8$$  

• $$-4$$  

• $$9$$