Chapter 3 Lesson 5 Solving 2-Step Equations Pgs. 120-124 What you will learn: To solve 2-step equations!

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Presentation transcript:

Chapter 3 Lesson 5 Solving 2-Step Equations Pgs What you will learn: To solve 2-step equations!

Background A two step equation contains two operations. In the equation 2x + 1 = 9, x is multiplied by 2 and then 1 is added. To solve two-step equations, use inverse operations to undo each operation in reverse order. You can solve 2x + 1 = 9 in two steps. Step 1: First, undo addition 2x + 1 = 9 2x = 9 -1 Subtract 1 from each side 2x = 8 Step 2: Undo the multiplication 2x = 8 2 2x = 4

How do you do the check of 2x + 1 = 9 if x = 4? Replace the x with 4 in the ORIGINAL Problem and solve step by step. 2(4) + 1 = = 9 9 = 9  This problem checks out!

Solve a two-step equation and check the solution. 5x - 2 = 13 Step 1: Undo the subtraction. 5x = x = 15 Step 2: Undo the multiplication 5x = x = 3 Check: 5x - 2 = 13 5(3) - 2 = = = 13 

Solve the equation and check the answer. 4 = n What do you do first? Undo the addition = n = n 6 What do you do next? Undo the division -7(6) = n (6) = n

Now check your answer In the original problem. 4 = n = = = 4  Remember, in order for a check to work out, both sides of the equation need to equal the same!!

Solve an equation with Negative coefficients 4 - x = 10 Think of the problem as 4 - 1x = x = x = x = -6 Check: 4 - x = (-6) = = 10 

Combine Like Terms before solving m - 5m + 3 = 47 Remember it can be rewritten as m + (-5m) + 3 = 47 Combine like terms: m - 5m + 3 = 47 -4m + 3 = 47 Subtract 3 from each side: -4m = Simplify: -4m = 44 Divide both sides by -4: -4m = Simplify: m = -11 Check: m - 5m + 3 = (-11) + 3 = = = = 47 

Use an equation to solve a problem A telephone calling card allows for 25¢ per minute plus a one-time service charge of 75 ¢. If the total cost of the card is $5, solve 25m + 75 = 500 to find the number of minutes you can use the card. Step 1: Undo the addition 25m = m = 425 Step 2: Undo the multiplication 25m = m = 17 Check: 25(17) + 75 = = = 500 

You try. Look at the questions Carefully! 3y + 4 = z = 11 3n + n - 4 = 12 3y = y = 9 3y = 9 y = z = z = z = 9 4n = n= n = 4 Check: 3(3) + 4 = = = 13  = = 11  3(4) = = 12 