Aim: How do we solve one-step equations?

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Presentation transcript:

Aim: How do we solve one-step equations? Do Now: Have a paper and pen/pencil on your desk to get ready for the quiz! Put your first and last name on the paper. The longer it takes for you to get ready, the shorter you have for your quiz so be prepared! Thank you.

Quiz! YOU DO NOT HAVE TO WRITE THE QUESTION!! 1. State the property that is illustrated by the equation a + b = b + a 2. Rational or irrational? 6 3. Rational or irrational? 1.12122122212222… 4. 12 + 8 (-2) – 3 2 5. 9 + 6●(8 - 5)

Solving an equation 3 + x = 5 What is the value of x?

x + 3 = 5 Do these equations still have the same solution as the equation above? Why or why not? 3 + x = 5 2) x + 3 + 2 = 5 + 2 3) x + 3 +5 = 10 4) 2x + 6 = 10

To solve one-step equations: Isolate the variable by using inverse operations to BOTH sides. Subtraction property of Equality- subtracting the same number from both sides produces an equivalent equation. x + 3 = 5 - 3 -3 x+ 0 = 2 x = 2

-Addition property of Equality- Adding the same number to each side of an equation maintains the balance of an equation. x -3 = 5

Multiplication property of Equality- multiplying each side of an equation by the same number produces an equivalent equation. x ÷ 4 = 4

10x = 40 Division property of Equality – dividing on each side of the equation by the same number produces an equivalent equation.

When solving one-step equations: x + 3 = 5 -When solving one-step equations: - what you do to one side you do to the other. - You need to keep the equations “balanced.” - you need to work backwards or “undo” what has been done by using the inverse operation. -isolate the variable - check your solution by substituting in the original equation!

Together! x – 2 = 5 3) 5x = 20 3 + x = 6 4) x ÷ 10 = 5

By yourselves! 12 – x = 6 3) 10 + x = 9 2) 3x = 12 4) x ÷4= 6

How do you think we should solve this? -x = 12

Solving multi-step equations Don’t forget to isolate the variable when you are solving an equation! 3x + 4 = 10 Use the property of equality for addition/subtraction. Use the property of equality for multiplication/division

Together! 17 = 8c – 7 3. 10 – x = 11 x ÷ 5 + 4 = 6

By yourselves! 3x + 5 = 35 3) 7x + 15 = 71 8 = 3c – 1 4) 2x + 3 = 15

Exit slip! 7 – x = 9 3x – 4 = 8