# Bell Ringer NWEA RIT band 231 240 Solving

Bell Ringer (NWEA) RIT band 231 -240

Solving Equations: variables on BOTH sides The student will be able to: 1. solve equations with variables on both sides. 2. solve equations containing grouping symbols.

1) Solve. 3 x + 2 = 4 x - 1 You need to get the variables on one side of the equation. It does not matter which variable you move. Try to move the one that will keep your variable positive.

Rules to remember • Simplify the left and the right separately – Use combining like terms and distribution • Solve by using inverse operations. • If you are moving anything over the equal sign, use inverse operations. If you are simplifying the separate sides, DO NOT use inverses

1. 2. 3. 4. 5. 6. 1) Solve 3 x + 2 = 4 x - 1 Draw “the river” - 3 x Subtract 3 x from 2 = x-1 both sides Simplify +1 +1 Add 1 to both sides 3 = x Simplify Check your 3(3) + 2 = 4(3) 1 answer 9 + 2 = 12 - 1

1. 2. 3. 4. 5. 6. 7. 8. 2) Solve 8 y - 9 = -3 y + 2 + 3 y Draw “the river” 11 y – 9 = 2 Add 3 y to both sides Simplify +9 +9 Add 9 to both sides Simplify 11 y = 11 Divide both sides by 11 Simplify 11 11 Check your answer y=1 8(1) - 9 = -3(1) + 2

What is the value of x if 3 - 4 x = 18 + x? 1. -3 2. 3. 4. 3 Answer Now

1. 3) Solve 4 = 7 x - 3 x Draw “the river” 4 = 4 x – Notice the variables 4 4 are on the same side! Combine like terms 1=x Divide both sides by 4 2. 3. 4. Simplify 5. Check your answer 4 = 7(1) - 3(1)

Let’s Throw in some Combining Like Terms!!!

That’s All for Today!!! • Please do your DLIQ!!!

Bell Ringer

Homework Review

YOU HAVE A QUIZ ON FRIDAY!!!!! • This quiz will cover the following: – 1 step Equations – 2 step easy equations – 2 step 2 “floor” equations – Multistep equations with variables on both sides

4) Solve -7(x - 3) = -7 1. Draw “the river” 2. Distribute 3. Subtract 21 from both sides 4. Simplify 5. Divide both sides by -7 6. Simplify 7. Check your answer -7 x + 21 = -7 - 21 -7 x = -28 -7 -7 x=4 -7(4 - 3) = -7 -7(1) = -7

What is the value of x if 3(x + 4) = 2(x - 1)? 1. 2. 3. 4. -14 -13 13 14 Answer Now

5) Solve 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Draw “the river” Clear the fraction – multiply each term by the LCD Simplify Add 2 x to both sides Simplify Add 6 to both sides Simplify Divide both sides by 6 Simplify Check your answer 3 - 2 x = 4 x – 6 + 2 x +2 x 3 = 6 x – 6 +6 +6 9 = 6 x 6 6 or 1. 5 = x

Special Case #1 6) 2 x + 5 = 2 x - 3 1. Draw “the river” 2. Subtract 2 x from both sides 3. Simplify -2 x 5 = -3 This is never true! No solutions

Special Case #2 7) 3(x + 1) - 5 = 3 x - 2 1. 2. 3. 4. Draw “the river” Distribute Combine like terms Subtract 3 x from both sides 5. Simplify 3 x + 3 – 5 = 3 x - 2 = 3 x – 2 -3 x -2 = -2 This is always true! Infinite solutions or identity

What is the value of x if -3 + 12 x = 12 x - 3? 1. 2. 3. 4. 0 4 No solutions Infinite solutions Answer Now

Challenge! What is the value of x if -8(x + 1) + 3(x - 2) = -3 x + 2? 1. 2. 3. 4. -8 -2 2 8 Answer Now

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