1. Solving 2-Step Equations
Grade 7 Pre-Algebra
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Let’s warm up :
Simplify:  
1) (3x - 5)(7x + 2)
2) (2a2 + 3)(5a - 3)
3) (2a + 3)(7a2 - 5)
4) (x + 5)(3x - 6)
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Let’s start
"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:  √ x or the "square root of x"; sqrt (x)
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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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5. You can solve the problem with the help of algebra tiles.
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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Now you try!
Solve x + 5 = 9
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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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Check:
3x – 6 = 15
3(7) – 6 = 15
21 – 6 = 15
15 = 15
Replace x with 7.
Multiply.
Simplify.
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Now you try!
Solve 15x + 3 = 48.
Check your solution.
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10. 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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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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Now you try!
Solve x + 13 = 11 4
Check your solution.
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13. 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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14. 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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Now you try!
Solve – x + 6 = 8.
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BREAK
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Solve each equation:
1) 2x - 8 = -10
2) 2x + 9 = 3
3) 4x - 6 = -18
4) 9x - 15 = 39
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Solve each equation:
5) x - 4 = 11 3
6) x + 2 = 0 3
7) - x = 25 5
8) 10 = 3 + x 2
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9) I bought three shirts that had equivalent retail values. I used a $15 gift certificate at the time of purchase and paid a total of $ How much did each individual shirt cost?
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10) Marty ordered three extremely accurate and scientific water-balloon launchers from a mail order catalog (one for himself and two for his friends). The total price including shipping charges was $50. If the total shipping cost was $5, how much did each launcher cost?
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Let’s review
"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: √x or the "square root of x"; sqrt (x)
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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.
Copyright © Ed2Net Learning, Inc.

24. 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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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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Check:
3x – 6 = 15
3(7) – 6 = 15
21 – 6 = 15
15 = 15
Replace x with 7.
Multiply.
Simplify.
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27. 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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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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29. 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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30. 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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Great Job!
Remember to do the practice worksheets!!!
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