Equations with Addition and Subtraction
Basics on the topic Equations with Addition and Subtraction
Solving Equations by Adding or Subtracting
What is an Equation? An equation tells us that the expression on either side of the equal sign is equal to the other. Sometimes, when writing an equation, you may have an unknown value that you need to solve for. A variable is a letter used to represent the value that we're solving for.
Equations can be used to solve word problems by following these steps:
Step #  What to do 

1  Read the word problem 
2  Highlight the important information 
3  Identify the operation 
4  Write the equation using a variable to represent the unknown value 
5  Solve the equation 
Solving Equations by Adding or Subtracting – Example
How do you solve addition and subtraction equations? Let’s take a look at the example from the video:
In order to reverse the experiment, Imani needs seventyeight ingredients altogether. The directions say they need twentyfour jars of mist and fourteen rose petals. The rest of the ingredients they need are crystals. How many crystals does Imani need?
Our equation is: twentyfour jars of mist plus fourteen rose petals plus c equals seventyeight because if we add all the ingredients together, the total number they need is seventyeight.
How to Solve an Equation by Adding or Subtracting
First, we add twenty four jars of mist and fourteen rose petals to get thirtyeight, but we still don't know how many crystals we need!
This is an addition equation, but since we do not know the value of c, we need to practice solving an addition equation using inverse operations.
The inverse operation of addition is subtraction, so we subtract thirtyeight from the number of ingredients in total, which is seventyeight. Seventyeight minus thirtyeight is forty, and we write the answer using the variable c equals forty.
Solving Equations by Adding or Subtracting – Summary
Remember an equation tells us that the expression on either side of the equal sign is EQUAL to the other. Equations can be used to solve word problems. When writing the equation we use a variable to represent the unknown value. Sometimes when solving equations with addition and subtraction you may have to use the inverse operation to find the answer. Always include the variable in your answer using an equal sign.
Want some more solving equations with addition and subtraction practice? On this website there are many interactive exercises for solving equations with addition and subtraction along with worksheets and other activities waiting to be completed.
Transcript Equations with Addition and Subtraction
Mr. Squeaks has time traveled to England and is spending a lot of time in this lab doing experiments. "Mr. Squeaks! What have you done?!" "Now I am Doctor Squeaks, if you want Mr. Squeaks back, you'll have to follow these directions!" In order for Imani to change Doctor Squeaks back to Mr. Squeaks, they need to follow the directions and solve... Equations with Addition and Subtraction. An equation tells us that the expression on either side of the equal sign (...) is EQUAL to the other. Equations can be used to solve word problems. First, Read the word problem. As you read, think; 'what do I need to find?'... and highlight the question you need to solve! For example... in order to reverse the experiment, Imani needs seventyeight ingredients altogether. The directions say they need twentyfour jars of mist and fourteen rose petals. The rest of the ingredients they need are crystals. How many crystals does Imani need? Here we highlight “How many crystals does Imani need?”... because it asks us to find how many crystals are needed to reverse the experiment. Now, reread and think; 'What is the important information?' While rereading, highlight keywords, numbers, or units of measurement, that will help answer the question. In the first sentence... highlight seventyeight ingredients altogether, (...) because this tells us the total number of ingredients they need. In the next sentence, highlight twentyfour jars of mist and fourteen rose petals (...) because this tells us how much of each ingredient they need. Also highlight, the rest of the ingredients they need are crystals (...) because that is the unknown value, or what we're trying to figure out. Then, identify the operation. We can't identify the operation just yet, so we move on to the next step. The next step is to write the equation using a VARIABLE to represent the unknown value. A variable is a letter used to represent the value that we're solving for. Our equation is: twentyfour jars of mist plus fourteen rose petals plus
Equations with Addition and Subtraction exercise

Complete the sentences.
HintsHere's an example of an equation.
The 'c' in this equation is a variable.
SolutionEquations tell us that the expression on either side of the equal sign is equal to the other.
Equations can be used to solve word problems.
We use variables to represent the unknown values in equations.

Solve the story problem.
HintsReread the problem and think: what is the important information?
Write the equation using a variable to represent the unknown value. Here we could use 'r' to represent the rose petals.
Add any numbers together first.
To solve for the variable, do the opposite operation to the answer. For example in 4 + b = 5, you would subtract 5  4 to solve for b.
SolutionAfter highlighting the important information shown, then this is the equation with the variable solved.
64 = 31 + 12 + r
31 + 12 = 43
64 = 43 + r
64  43 = r
21 = r
So, 21 rose petals are needed. 
Solve for each variable.
HintsRemember, you are solving for the variable, or the letter. In all of these equations it is x.
Add any numbers together first.
To solve for the variable, do the opposite operation to the answer.
For example in 4 + x = 5, you would subtract 5  4 to solve for x.
Another strategy to check your answer is to plug in the number for x to see if it's correct.
Solutionx + 10 = 25
x = 25  10
x = 1537 = 26 + x
37  26 = x
x = 1113 + 22 + x = 42
13 + 22 = 35
35 + x = 42
x = 42  35
x = 757 = 32 + 12 + x
32 + 12 = 44
57 = 44 + x
57  44 = x
x = 13 
Solve each story problem.
HintsReread the problem and think: what is the important information?
Write the equation using a variable to represent the unknown value.
Add any numbers together first.
To solve for the variable, do the opposite operation to the answer. For example in 4 + b = 5, you would subtract 5  4 to solve for b.
SolutionFor the first problem:
27 + 36 + x = 72
27 + 36 = 63
63 + x = 72
x = 72  63
x = 9, so 9 jars of mist.
For the second problem:
65 = 22 + 32 + x
22 + 32 = 54
65 = 54 + x
65  54 = x
11 = x, so 11 leaves . 
Solve for the variable.
HintsRemember, you are solving for the variable, or the letter.
Add any numbers together first.
To solve for the variable, do the opposite operation to the answer. For example in 4 + b = 5, you would subtract 5  4 to solve for b.
Solution13 + 25 + b = 50
13 + 25 = 38
38 + b = 50
b = 50  38
b = 12 
Solve each story problem.
HintsReread the problem and think: what is the important information?
Write the equation using a variable to represent the unknown value.
Add any numbers together first.
To solve for the variable, do the opposite operation to the answer. For example in 4 + b = 5, you would subtract 5  4 to solve for b.
SolutionFor the first smoothie:
17 + 44 + b = 75
17 + 44 = 61
61 + b = 75
b = 75  61
b = 14, so that answer was correct.
For the second smoothie:
64 = 32 + 18 + r
32 + 18 = 50
64 = 50 + r
64  50 = r
14 = r, so that answer was incorrect.
For the last smoothie:
52 = 19 + 27 + i
19 + 27 = 46
52 = 46 + i
52  46 = i
6 = i, so that answer was incorrect.