chapter 3 lesson 5 solving 2-step equations pgs. 120-124 what you will learn: to solve 2-step...
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Chapter 3 Lesson 5Solving 2-Step Equations
Pgs. 120-124
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 2and then 1 is added. To solve two-step equations,use inverse operations to undo each operation inreverse order. You can solve 2x + 1 = 9 in twosteps.
Step 1: First, undo addition2x + 1 = 9
2x + 1 -1 = 9 -1 Subtract 1 from each side 2x = 8
Step 2: Undo the multiplication2x = 82x = 8 2 2 x = 4
How do you do the check of 2x + 1 = 9 if x = 4?
Replace the x with 4 in the ORIGINALProblem and solve step by step.
2(4) + 1 = 9 8 + 1 = 9 9 = 9
This problem checks out!
Solve a two-step equation andcheck the solution.
5x - 2 = 13
Step 1: Undo the subtraction. 5x - 2 +2 = 13 +2
5x = 15
Step 2: Undo the multiplication 5x = 15
5x = 15 5 5 x = 3
Check: 5x - 2 = 13 5(3) - 2 = 13 15 - 2 = 13 13 = 13
Solve the equation and check the answer.
4 = n + 11 6
What do you do first? Undo the addition
4 - 11 = n + 11 -11 6
-7 = n 6
What do you do next? Undo the division
-7(6) = n (6) 6 -42 = n
Now check your answerIn the original problem.
4 = n + 11 64 = -42 + 11 6
4 = -7 + 11
4 = 4
Remember, in order for a check to work out, both sides of the equation needto equal the same!!
Solve an equation withNegative coefficients
4 - x = 10
Think of the problem as 4 - 1x = 10 4 - 4 - 1x = 10 - 4
-1x = 6
-1x = 6 -1 -1
x = -6
Check: 4 - x = 10 4 - (-6) = 10
10 = 10
Combine Like Terms beforesolving
m - 5m + 3 = 47 Remember it can be rewrittenas m + (-5m) + 3 = 47
Combine like terms: m - 5m + 3 = 47 -4m + 3 = 47
Subtract 3 from each side: -4m + 3 - 3 = 47 - 3Simplify: -4m = 44
Divide both sides by -4: -4m = 44 -4 -4
Simplify: m = -11Check: m - 5m + 3 = 47
-11 - 5(-11) + 3 = 47 -11 + 55 + 3 = 47
44 + 3 = 47 47 = 47
Use an equation to solve aproblem
A telephone calling card allows for 25¢ perminute plus a one-time service charge of 75¢. If thetotal 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 + 75 -75 = 500 -75
25m = 425
Step 2: Undo the multiplication25m = 425 25 25
m = 17
Check:25(17) + 75 = 500425 + 75 = 500 500 = 500
You try. Look at the questionsCarefully!
3y + 4 = 13
20 - z = 11
3n + n - 4 = 12
3y + 4 -4 = 13 - 43y = 93y = 9 y = 3 3 3
20 - 20 - z = 11 - 20-z = -9 -z = -9 -1 -1 z = 9
4n - 4 + 4 = 12 + 44n= 16 4n = 16 4 4 n = 4
Check:3(3) + 4 = 13 9 + 4 = 13 13 = 13
20 - 9 = 11 11 = 11
3(4) + 4 - 4 = 12 12 = 12