This = That
Basics
An algebraic equation is a particular type of algebraic expression using the = sign.
An equation means This = That
Whatever is on the left side of an equation = Whatever is on the right side of an equation
Whatever is done to the left side of an equation (add, subtract, multiply, divide) =
Whatever is done to the right side of an equation (add, subtract, multiply, divide)
A question involving an equation often means solving for the numerical value of a variable.
When solving:
• It is helpful to isolate the variable in question on the left side of the equation.
• It is helpful to perform a mathematical operation that is the opposite of the equation’s original mathematical operation.
• It is helpful to know your multiplication and division tables. However, the TI30XS MultiView Scientific Calculator can be used as needed.
• For the sake of order of operations, it is better to set up division language in form rather than x÷y form.
Question
Given x + 3 = 8, solve for x.
Answer
x = 5
Answer Process
x + 3 = 8
x + 3 – 3 = 8 – 3
• 3 is subtracted from each side of = sign
• subtraction is the opposite of addition
x = 5
• 3 – 3 is the same as 0, so it disappears
• 8 – 3 is the same as 5
• x has been isolated on the left side of = sign
Question
Given x – 3 = 8, solve for x.
Answer
x = 11
Answer Process
x – 3 = 8
x – 3 + 3 = 8 + 3
• 3 is added to each side of = sign
• addition is the opposite of subtraction
x = 11
• 3 + 3 is the same as 0, so it disappears
• 8 + 3 is the same as 11
• x has been isolated on the left side of = sign
Question
Given 3y = 27, solve for y.
Answer
y = 9
Answer Process
3y = 27
=
• each side of = sign is divided by 3
• division is the opposite of multiplication
y = 9
• is the same as 1y which is the same as y
• is the same as 9
• y has been isolated on the left side of = sign
Question
Given = 4, solve for y.
Answer
y = 20
Answer Process
= 4
= 5·4
• each side of = sign is multiplied by 5
• multiplication is the opposite of division
y = 20
• is the same as 1y which is the same as y
• 5·4 is the same as 20
• y has been isolated on the left side of = sign
Question
Given 5y + 6 = 26, solve for y.
Answer
y = 4
Answer Process
5y + 6 = 26
5y + 6 – 6 = 26 – 6
• 6 is subtracted from each side of = sign
• subtraction is the opposite of addition
5y = 20
• 6 – 6 is the same as 0, so it disappears
• 26 – 6 is the same as 20
=
• each side of = sign is divided by 5
• division is the opposite of multiplication
y = 4
• is the same as 1y which is the same as y
• is the same as 4
• y has been isolated on the left side of = sign
Question
Given – 3 = 5, solve for y.
Answer
y = 56
Answer Process
– 3 = 5
– 3 + 3 = 5 + 3
• 3 is added to each side of = sign
• addition is the opposite of subtraction
= 8
• 3 + 3 is the same as 0, so it disappears
• 5 + 3 is the same as 8
= 7·8
• each side of = sign is multiplied by 7
• multiplication is the opposite of division
y = 56
• is the same as 1y which is the same as y
• 7·8 is the same as 56
• y has been isolated on the left side of = sign
Calculator Click  What You See  Comment 
blinker  clears screen  
5 + 3  5+3  addition on right side of = 
8  
7 × 8  7*8  multiplication on right side of = 
56  Answer  
Equation 
Question
Given 16y + 6 = 126, solve for y in decimal form.
Answer
y = 7.5
Answer Process
16y + 6 = 126
16y + 6 – 6 = 126 – 6
• 6 is subtracted from each side of = sign
• subtraction is the opposite of addition
16y = 120
• 6 – 6 is the same as 0, so it disappears
• 126 – 6 is the same as 120
=
• each side of = sign is divided by 16
• division is the opposite of multiplication
y = 7.5
• is the same as 1y which is the same as y
• is the same as which is the same as 7.5 (after toggle)
• y has been isolated on the left side of = sign
Calculator Click  What You See  Comment 
blinker  clears screen  
126 – 6  1266  subtraction on right side of = 
120  
120 16  division on right side of =  
7.5  Answer (Toggle) 

Equation 
Question
Five collectors threw away 4 worthless stamps at a trade show. Each collector ended up with 26 stamps.
Given the equation – 4 = 26, how many total stamps s were originally distributed among the 5 collectors?
Answer
s = 150
Answer Process
– 4 = 26
– 4 + 4 = 26 + 4
• 4 is added to each side of = sign
• addition is the opposite of subtraction
= 30
• 4 + 4 is the same as 0, so it disappears
• 26 + 4 is the same as 30
= 5·30
• each side of = sign is multiplied by 5
• multiplication is the opposite of division
s = 150
• is the same as 1s which is the same as s
• 5·30 is the same as 150
• s has been isolated on the left side of = sign
Calculator Click  What You See  Comment 
blinker  clears screen  
26 + 4  26+4  addition on right side of = 
30  
5 × 30  5*30  multiplication on right side of = 
130  Answer  
Equation 
Question
A landscaping crew planted 12 trees an hour plus an additional 7 trees for a total of 223 trees.
Given the equation 12h + 7 = 223, how many hours h did the crew spend planting?
Answer
h = 18
Answer Process
12h + 7 = 223
12h + 7 – 7 = 223 – 7
• 7 is subtracted from each side of = sign
• subtraction is the opposite of addition
12h = 216
• 7 – 7 is the same as 0, so it disappears
• 223 – 7 is the same as 216
=
• each side of = sign is divided by 12
• division is the opposite of multiplication
h = 18
• is the same as 1h which is the same as h
• is the same as 18
• h has been isolated on the left side of = sign
Calculator Click  What You See  Comment 
blinker  clears screen  
223 – 7  2237  subtraction on right side of = 
216  
216 12  division on right side of =  
18  Answer  
Equation 
Practice – Questions
1. Given x + 4 = 18, solve for x.
2. Given x – 4 = 12, solve for x.
3. Given – 4 = 3, solve for y.
4. Given 16y + 8 = 146, solve for y in decimal form.
5. Five hobbyists threw away 3 worthless baseball cards at a trade show. Each hobbyist ended up with 22 baseball cards. Given the equation – 3 = 22, how many total cards c were originally distributed among the 5 hobbyists?
6. Four regular umpires umpired 39 games apiece during the baseball season. Two extra games were umpired by substitute umpires. Given the equation + 2 = 39, how many total games g were umpired?
7. A dog collected 15 good bones a day plus 8 bones unworthy of keeping for a total of 158 bones. Given the equation 15d + 8 = 158, how many days d did the dog spend collecting bones?
8. A teacher concocted 10 original test questions an hour minus 5 duplicate questions for a total of 125 test questions. Given the equation 10h – 5 = 125, how many hours h did the teacher spend concocting test questions?
9. A bird intended to fly 979 miles. The bird covered 14 miles an hour before stopping 43 miles short to swim in a pond. Given the equation 14h – 43 = 979, how many hours h did it take the bird to reach the pond?
10. A shopper spent $96.00 at the mall, including $5.00 for parking. The shopper spent $7.00 apiece on accessories. Given the equation 7a + 5 = 96, how many accessories a did the shopper buy?
Practice – Answers
1. x = 14
2. x = 16
3. y = 35
4. y = 8.625
5. c = 125
6. g = 148
7. d = 10
8. h = 13
9. h = 73
10. a = 13
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