1. Solving Multi-Step Equations
Good Afternoon!
Today we will be learning about
Solving Multi-Step Equations
Let’s warm up :
Simplify:  
1) x = 3
1) 3x - 5 = 10
2) a = 6
2) 4a + 3 = 27
3) y + 3 = 6 7
3) y = 21
4) m - 3 = 9 5
4) m = 60
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2. Solving 2-Step Equations
Let’s review with
Solving 2-Step Equations
"Linear" equations are mathematical expressions that have an equal sign and linear expressions
However, variable(s) in linear equations:
Cannot have exponents (or powers) For example, x squared or x 2
Cannot multiply or divide each other For example:  "x" times "y" or xy; "x" divided by "y" or x/y
Cannot be found under a root sign or square root sign (sqrt) For example:  Ö x or the "square root of x"; sqrt (x)
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3. Copyright © Ed2Net Learning, Inc.
Review
It takes two steps to solve an equation or inequality that has more than one operation:
Simplify using the inverse of addition or subtraction.
Simplify further by using the inverse of multiplication or division.
When you multiply or divide an inequality by a negative number, you must reverse the inequality symbol.
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4. You can solve the problem with the help of algebra tiles.
Review
Solve 2x + 1 = 5
You can solve the problem with the help of algebra tiles.
2x + 1 = 5
Model the equation.
Remove 1 tile from each side.
2x + 1 – 1 = 5 – 1
2x = 4
Divide each side into two equal groups.
2x = 4
Simplify.
x = 2
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5. Copyright © Ed2Net Learning, Inc.
Review
To solve a two-step equation, first undo addition or subtraction. Then undo multiplication or division.
Solve 3x – 6 = 15.
Check your solution.
3x – 6 = 15
3x – =
3x = 21
x = 7
Add 6 to each side.
Simplify.
Divide each side by 3.
Simplify.
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6. Copyright © Ed2Net Learning, Inc.
Review
Check:
3x – 6 = 15
3(7) – 6 = 15
21 – 6 = 15
15 = 15
Replace x with 7.
Multiply.
Simplify.
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7. Review Solve x - 19 = 17. 4 Check your solution. x - 19 = 17 4
Add to undo the subtraction.
Multiply to undo the division.
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8. Copyright © Ed2Net Learning, Inc.
Review
Check:
x - 19 = 17 4
= 17
= 17
17 = 17
Replace x with 144.
Do the division first.
The solution is 144.
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9. Let the cost of 1 ticket for a child is = x
Five children and one adult went to a concert. Adult tickets were $14. The total price for all the tickets was $59. What was the cost of each child’s ticket?
Let the cost of 1 ticket for a child is = x
Adult tickets were = $14
Total price for the tickets for five children and one adult = $59,
Hence,
5x + 14 = 59
5x + 14 – 14 = 59 – 14
5x = 45
x = 9
Subtract to undo the addition.
Divide to undo the multiplication.
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10. Negative Coefficients
Review
Negative Coefficients
Solve 5 – x = 17.
5 – x = 17
– x =
0 – x = 12
–x = 12
-1(–x) = -1(12)
x = -12
Add -5 to each side.
Simplify.
0 – x = -x
Multiply each side by -1.
Simplify.
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11. Solving Multi-Step Equations
Let’s start with
Solving Multi-Step Equations
Most linear equations require more than one step for their solution.
Just as with solving one-step or two-step or any equation, one goal in solving an equation is to have only variables on one side of the equal sign and numbers on the other side of the equal sign.
The other goal is to have the number in front of the variable (i.e., coefficient) equal to one.
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12. Steps for solving a Multi-step Equation:
Step1: Use the Distributive Property wherever necessary.
Step2: Combine like terms.
Step3: Undo addition or subtraction.
Step4: Undo multiplication or division.
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13. You can solve the problem with the help of algebra tiles.
Solve 2x x = 14
You can solve the problem with the help of algebra tiles.
2x x = 14
Group the tiles so that all the ‘x’ tiles are together.
3x + 5 = 14
Next slide.
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14. Remove 5 tiles from each side.
3x = 9
Divide each side into three equal groups.
3x = 9
Simplify.
x = 3
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15. Copyright © Ed2Net Learning, Inc.
Now you try!
Solve:
1) 8x + 4x = 144
2) 9x - 2x = -42
1) x = 12
2) x = -6
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16. You may need to use the Distributive property when you solve a multi-step equation.
Solve: 2(5x - 3) = 14
2(5x - 3) = 14
10x - 6 = 14
10x =
10x = 20
x = 2
Use the Distributive property.
Add 6 to each side.
Simplify.
Divide each side by 10.
Simplify.
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17. Solve: 38 = -3(4y + 2) + y 38 = -3(4y + 2) + y 38 = - 12y - 6 + y
-4 = y
Use the Distributive property.
Use the Commutative and Associative properties of addition to group like terms.
Combine like terms.
Add 6 to each side.
Simplify.
Divide each side by -11.
Simplify.
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18. Copyright © Ed2Net Learning, Inc.
Now you try!
Solve:
1) -3(m - 6) = 3
2) 3(x + 12) - x = 8
1) m = 5
2) x = -14
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19. Copyright © Ed2Net Learning, Inc.
Real world problems
Jake and Suki collect model airplanes. Suki has four fewer than twice as many model airplanes as Jake. Together they have 14 models. Solve the equation m + 2m - 4 = 14. Find the number of models each person has.
m + 2m - 4 = 14
3m - 4 = 14
3m =
3m = 18
m = 6
Combine like terms.
Add 4 to each side.
Simplify.
Divide each side by 3.
Simplify.
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20. Finding consecutive integers
The sum of three consecutive integers is 96. Find the integers.
Sum of three consecutive integers =
Let, n = the least integer.
Then n + 1 = the second integer.
And n + 2 = the third integer.
Hence, the equation is:
n + (n + 1) + (n + 2) = 96
Next slide.
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21. Copyright © Ed2Net Learning, Inc.
Solution
n + (n + 1) + (n + 2) = 96
(n + n+ n) + (1 + 2) = 96
3n + 3 = 96
3n =
3n = 93
n = 31
Use the Commutative and Associative properties of addition to group like terms.
Combine like terms.
Subtract 3 from each side.
Simplify.
Divide each side by 3.
Simplify.
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22. 1) The sum of four consecutive integers is 358. Find the integers.
Now you try!
1) The sum of four consecutive integers is 358. Find the integers.
1) 88, 89, 90, 91
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23. Copyright © Ed2Net Learning, Inc.
BREAK
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24. GAME
Click on the link below for some exciting puzzle
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25. Copyright © Ed2Net Learning, Inc.
Assignment
Solve each equation:
1) 5b b = 50
1) b = 13
2) 4a a = 19
2) a = 6
3) 18 = b - 7b
3) b = -3
4) 4d + 2d - 3d = 27
4) d = 9
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26. Copyright © Ed2Net Learning, Inc.
Solve each equation:
5) 3(n - 2 ) = 36
5) n = 14
6) 4(y - 1 ) = 36
6) y = 10
7) 2(8 + n) = 22
7) n = 3
8) -2(a + 3) - a = 0
8) a = 3
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27. 9) The sum of two consecutive integers is 131. Find the integers.
9) 65, 66
9) The sum of two consecutive integers is 131. Find the integers.
10) The sum of three consecutive even integers is 60. Find the integers.
10) 19, 20, 21
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28. Copyright © Ed2Net Learning, Inc.
11) One basketball team defeated another by 13 points. The total number of points scored by both teams was 171 to find the number of points p scores by the winning team?
11) 92
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29. Solving Multi-Step Equations
Let’s review
Solving Multi-Step Equations
Steps for solving a Multi-step Equation:
Step1: Use the Distributive Property wherever necessary.
Step2: Combine like terms.
Step3: Undo addition or subtraction.
Step4: Undo multiplication or division.
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30. You can solve the problem with the help of algebra tiles.
Review
Solve 2x x = 14
You can solve the problem with the help of algebra tiles.
2x x = 14
Group the tiles so that all the ‘x’ tiles are together.
3x + 5 = 14
Next slide.
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31. Remove 5 tiles from each side.
Review
Remove 5 tiles from each side.
3x = 9
Divide each side into three equal groups.
3x = 9
Simplify.
x = 3
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32. You may need to use the Distributive property when you solve a multi-step equation.
Review
Solve: 2(5x - 3) = 14
2(5x - 3) = 14
10x - 6 = 14
10x =
10x = 20
x = 2
Use the Distributive property.
Add 6 to each side.
Simplify.
Divide each side by 10.
Simplify.
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33. Solve: 38 = -3(4y + 2) + y Review 38 = -3(4y + 2) + y
-4 = y
Use the Distributive property.
Use the Commutative and Associative properties of addition to group like terms.
Combine like terms.
Add 6 to each side.
Simplify.
Divide each side by -11.
Simplify.
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34. Copyright © Ed2Net Learning, Inc.
Review
Real world problems
Jake and Suki collect model airplanes. Suki has four fewer than twice as many model airplanes as Jake. Together they have 14 models. Solve the equation m + 2m - 4 = 14. Find the number of models each person has.
m + 2m - 4 = 14
3m - 4 = 14
3m =
3m = 18
m = 6
Combine like terms.
Add 4 to each side.
Simplify.
Divide each side by 3.
Simplify.
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35. Finding consecutive integers
Review
Finding consecutive integers
The sum of three consecutive integers is 96. Find the integers.
Sum of three consecutive integers =
Let, n = the least integer.
Then n + 1 = the second integer.
And n + 2 = the third integer.
Hence, the equation is:
n + (n + 1) + (n + 2) = 96
Next slide.
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36. Copyright © Ed2Net Learning, Inc.
Review
Solution
n + (n + 1) + (n + 2) = 96
(n + n+ n) + (1 + 2) = 96
3n + 3 = 96
3n =
3n = 93
n = 31
Use the Commutative and Associative properties of addition to group like terms.
Combine like terms.
Subtract 3 from each side.
Simplify.
Divide each side by 3.
Simplify.
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37. See you in the next session.
You have done a nice job.
See you in the next session.
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