Solving Multi-Step Equations

Solving Multi-Step Equations

OBJ: To solve equations that involve multiple steps using inverse operations and S A D M E P

Topics to Review

1. Distributive Property
2. Combining Like Terms
3. Solving Two-Step Equations
4. Solving One-Step Equations

Distributive Property

Multiple Choice

 $Simplify:\ \ -3\left(2x\ -\ 5\right)$  

•  $9x$  

•  $-6x\ +\ 15$  

•  $-6x\ -5$  

•  $-6x-15$  

Combining Like Terms

Like terms have the same variable parts.

All constants are like terms.

Only like terms can be combined by addition or subtraction.

Multiple Choice

 $Simplify:\ 4x\ -\ 7\ -5x\ +3x$  

•  $2x\ -\ 7$  

•  $-5x$  

•  $-12x\ -7$  

•  $-4x-7$  

Multiple Choice

 $Simplify:\ 5\left(3x\ -\ 1\right)\ -8+x$  

•  $20x-45$  

•  $11x-8$  

•  $16x-9$  

•  $16x-13$  

Special Cases of Linear Equations

Rules for Solving Multi-Step Equations

1. Distribute if you have any distributive property
2. Combine Like Terms on the SAME SIDE of the equation
3. Get the variable terms together on one side of the equation
4. Get the constants together on the opposite side of the equation
5. Solve the resulting one-step equation using multiplication or division
6. CHECK YOUR SOLUTION!!!!

Special Case for Equations (No Solution)

If the variables drop out and you are left with a false statement, then the equation has NO SOLUTION!

ex. If you solve the equation and all that is left is -2 = 6 would mean the equation has no solution.

Special Case for Equations (Infinite Solutions)

If the variables drop out and you are left with a TRUE statement, then the equation has INFINITE SOLUTIONS!

ex. If you solve the equation and all that is left is 6 = 6 would mean the equation has infinite solutions.

Multiple Choice

 $Solve:\ 3x\ -9\ =2x\ +6\ +\ x$  

• No Solution

• Infinite Solutions

Multiple Choice

 $Solve:\ -\left(4-y\right)\ =y\ -5+1$  

• No Solution

• Infinite Solutions

Rules for Solving Multi-Step Equations

1. Distribute if you have any distributive property
2. Combine Like Terms on the SAME SIDE of the equation
3. Get the variable terms together on one side of the equation
4. Get the constants together on the opposite side of the equation
5. Solve the resulting one-step equation using multiplication or division
6. CHECK YOUR SOLUTION!!!!

Fill in the Blank

 $Solve:\ \ -12=2+5d+2d$  

Fill in the Blank

 $Solve:\ \ 3f+7=5f-13$  

Fill in the Blank

 $Solve:\ \ 3\left(4-6w\right)+9=-15w+30$  

Today's Assignment

Complete Solving Multi-Step Equations Quizizz

Use the reference slide as needed

You may retry the Quizizz as many times as you wish by 11/18