3292017 I can solve multistep equations Quiz Friday

3/29/2017 I can solve multi-step equations.

Quiz Friday • -Two step equations • -Multi-step equations with the distributive property • -Two-step equation word problems

Remember! • Distrubute first if you can • Use inverse operations to undo addition/subtraction first, then multiplication/division • Remember…if a number is 2 x that means 2 multiplied by x! • Remember…if a number is x/4 that means x divided by 4 • If a number is ¼ x you undo it by multiplying by the reciprocal i. e. 4/1

Try These Examples 1. 2 x – 5 = 17 2. 3 y + 7 = 25 3. 5 n – 2 = 38 4. 12 b + 4 = 28

Check your answers!!! 1. x = 11 2. y = 6 3. n = 8 4. b = 2

Ready to Move on?

Ex. 2: Solve x/3 + 4 = 9 -4 -4 x/3 = 5 (Subt. 4 from both sides) (Simplify) (x/3) 3 = 5 3 (Mult. by 3 on both sides) x = 15 (Simplify)

Try these examples! 1. x/5 – 3 = 8 2. c/7 + 4 = 9 3. r/3 – 6 = 2 4. d/9 + 4 = 5

Check your answers!!! 1. x = 55 2. c = 35 3. r = 24 4. d = 9

Solving equations using the Distributive Property • When solving equations, sometimes you will need to use the distributive property first. • At this level you are required to be able to recognize and know how to use the distributive property • Essentially, you multiply what’s on the outside of the parenthesis with EACH term on the inside of the parenthesis • Let’s see what that looks like…

Example #3 5 x + 3(x +4) = 28 In this instance I begin on the left side of the equation I recognize the distributive property as 3(x +4). I must simplify that before I can do anything else 5 x + 3(x +4) = 28 5 x +3 x +12 = 28 After I do the distributive property I see that I have like terms (5 x and 3 x) I have to combine them to get 8 x before I can solve this equation

Distributing a Negative • Distributing a negative number is similar to using the distributive property. • However, students get this wrong because they forget to use the rules of integers • Quickly the rules are…when multiplying, if the signs are the same the answer is positive. If the signs are different the answer is negative

Example #4 4 x – 3(x – 2) = 21 I begin by working on the left side of the equation. In this problem I have to use the distributive property. However, the 3 in front of the parenthesis is a negative 3. When multiplying here, multiply the -3 by both terms within the parenthesis. Use the rules of integers 4 x – 3(x – 2) = 21 4 x – 3 x + 6 = 21 After doing the distributive property, I see that I can combine the 4 x and the -3 x to get 1 x or x

Your Turn 1. 2. 3. 4. 2 x + 7 = 15 6 = 14 – 2 x 3(x – 2) = 18 12(2 – x) = 6

Your Turn Solutions 2. 3. 4. 5. 4 4 8 1½

• 1. -3(1 x+5)=10 • 2. -4(3 x+2)=12 • 3. 3(2 x-3)=15

• 1. -5(4 x+2)=-10 • 2. -2(1 x+2)=12 • 3. 5(5 x-3)=18