Sample Problem: Solving Algebraic Equations

Example:

• a + 1 = 3
• a = 3 - 1
• If you transpose a certain value to the other side of the equation, it "becomes the opposite of the original," so plus becomes minus, minus becomes plus, multiply becomes divide and vice versa.
• a = 2
• 2 + 1 = 3
• 3 = 3
• a = 2

Sample Problems:

• Solve for a:
• 5 + a = 7
• a - 13 = 4
• 3a  = 9
• a/2 = 10
• Solve for b:
•  9 + b = 15
• b - 2 = 1
• 2b = 2
• b/3 = 4
• Solve for c:
• 6 + c = 13
• c - 3 = 2
• 2c = 20
• 6/c = 3
• Solve for x: 
• 2 + x = 24
• x - 3 = 20
• 8x = 16
• x/7 = 5
• Solve for y:
• 8 + y = 28
• y - 4 = 12
• 3y = 15
• y/8 = 2

Sample Problem: Substituting Variables

Example Problem:

• What is the value of a + 1 if:
• a = 1
• a = 2
• a = 3
• a = 4
• a = 5

Answer to Example Problem:

• a + 1 =
• 2
• 3
• 4
• 5
• 6

Sample Problems:

• What is j + 7 if...
• j = 5
• j = 9
• j = 6
• What is u + 5 if...
• u = 4
• u = 2
• u = 8
• What is d + 9 if...
• d = 5
• d = 2
• d = 11
• What is b + 6 if...
• b = 1
• b = 4
• b = 3
• What is x + 8 if...
• x = 1
• x = 2
• x = 3

Sample Problems: Variables

Here are some sample problems regarding the previous discussed topic: Variables.
Try to answer the following orally and as fast as you can. Ready... get set... go!

• Try to identify the variable(s) in the following expressions:
• a) 7j + 8
• b) 5x - 2
• c) 9a + 3b
• If x represents the number of meters Nick sprinted for gym class, make an expression for:
• a) The distance Nick sprinted, doubled.
• b) Half of the distance Nick sprinted.
• c) The distance Nick sprinted, plus an additional 10 meters.
• If y represents the number of hours Jane spent sleeping, make an expression for:
• a) 5 hours more than the number of hours Jane slept
• b) Twice the time Jane spent sleeping
• c) Twice Jane's time sleeping, plus 5 more hours
• If z represents the number of gun shots James fired, make an expression for:
• a) The number of shots James would have made if she fired 8 more shots.
• b) The number of shots James would have made if she only fired half of the total shots she did.
• c) The number of shots James would have made if she fired 3 less shots.
• If x represents the amount of money (in PHP) Julia spent at the bookstore, make an expression for:
• a) The amount of money she would have spent if she bought one more book worth 280 pesos.
• b) The amount of money she would have spent if she didn't buy the book worth 150 pesos.
• c) The amount of money she would have spent if she had spent twice as much, and bought an additional book on sale for 75 pesos.

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