Linear Equations with Whole Numbers - Basic Math
Card 1 of 56
Roman is ordering uniforms for the tennis team. He knows how many people are on the team and how many uniforms come in each box. Which equation can be used to solve for how many boxes 
Roman should order?
Roman is ordering uniforms for the tennis team. He knows how many people are on the team and how many uniforms come in each box. Which equation can be used to solve for how many boxes
Tap to reveal answer
The total number of uniforms needed equals the number of students divided by the number of uniforms per box.
The total number of uniforms needed equals the number of students divided by the number of uniforms per box.
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Dr. Jones charges a $50 flat fee for every patient. He also charges his patients $40 for every 10 minutes that he spends with him. If Mrs. Smith had an appointment that lasted 30 minutes, how much did she have to pay Dr. Jones?
Dr. Jones charges a $50 flat fee for every patient. He also charges his patients $40 for every 10 minutes that he spends with him. If Mrs. Smith had an appointment that lasted 30 minutes, how much did she have to pay Dr. Jones?
Tap to reveal answer
We can express Dr. Jones's rate in a linear equation:
Since Mrs. Smith's appointment lasted 30 minutes, we have 3 10-minute intervals. Then, we can plug in that number into our above equation to find out how much the appointment cost.
We can express Dr. Jones's rate in a linear equation:
Since Mrs. Smith's appointment lasted 30 minutes, we have 3 10-minute intervals. Then, we can plug in that number into our above equation to find out how much the appointment cost.
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Jimmy had 
in lunch money for school. Everyday he spends 
for food and drinks. What is the expression that shows how much money will he have after each day, where 
is the days, and 
is the total amount of money left?
Jimmy had
Tap to reveal answer
Jimmy starts off with $60, and spends $3.50 everyday.
This means that he will have $56.50 after day 1, $53 after day 2, and so forth.
Only one equation satisfies this scenario. The rest are irrelevant.
Jimmy starts off with $60, and spends $3.50 everyday.
This means that he will have $56.50 after day 1, $53 after day 2, and so forth.
Only one equation satisfies this scenario. The rest are irrelevant.
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What is the solution of 
that satisfies both equations?
What is the solution of
Tap to reveal answer
Reduce the second system by dividing by 3.
Second Equation:
We this by 3.
Then we subtract the first equation from our new equation.
First Equation:
First Equation - Second Equation:
Left Hand Side:
Right Hand Side:
Our result is:
Reduce the second system by dividing by 3.
Second Equation:
Then we subtract the first equation from our new equation.
First Equation:
First Equation - Second Equation:
Left Hand Side:
Right Hand Side:
Our result is:
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What is the solution of 
for the systems of equations?
What is the solution of
Tap to reveal answer
We add the two systems of equations:
For the Left Hand Side:
For the Right Hand Side:
So our resulting equation is:
Divide both sides by 10:
For the Left Hand Side:
For the Right Hand Side:
Our result is:
We add the two systems of equations:
For the Left Hand Side:
For the Right Hand Side:
So our resulting equation is:
Divide both sides by 10:
For the Left Hand Side:
For the Right Hand Side:
Our result is:
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What is the solution of 
for the two systems?
What is the solution of
Tap to reveal answer
We first multiply the second equation by 4.
So our resulting equation is:
Then we subtract the first equation from the second new equation.
Left Hand Side:
Right Hand Side:
Resulting Equation:
We divide both sides by -15
Left Hand Side:
Right Hand Side:
Our result is:
We first multiply the second equation by 4.
So our resulting equation is:
Then we subtract the first equation from the second new equation.
Left Hand Side:
Right Hand Side:
Resulting Equation:
We divide both sides by -15
Left Hand Side:
Right Hand Side:
Our result is:
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What is the solution of 
for the two systems of equations?
What is the solution of
Tap to reveal answer
We first add both systems of equations.
Left Hand Side:
Right Hand Side:
Our resulting equation is:
We divide both sides by 3.
Left Hand Side:
Right Hand Side:
Our resulting equation is:
We first add both systems of equations.
Left Hand Side:
Right Hand Side:
Our resulting equation is:
We divide both sides by 3.
Left Hand Side:
Right Hand Side:
Our resulting equation is:
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Solve for 
.
Solve for
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First, add 6 to both sides so that the term with "x" is on its own.
Now, divide both sides by 2.
First, add 6 to both sides so that the term with "x" is on its own.
Now, divide both sides by 2.
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Solve:
Solve:
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The answer is 
. The goal is to isolate the variable, 
, on one side of the equation sign and have all numerical values on the other side of the equation.
Since 
is a negative number, you must add 
to both sides.
Then, divide both sides of the equation by 
:
The answer is
Since
Then, divide both sides of the equation by
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Solve for 
.
Solve for
Tap to reveal answer
Start by isolating the term with 
to one side. Add 10 on both sides.
Divide both sides by 7.
Start by isolating the term with
Divide both sides by 7.
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If 
, what is 
equal to?
If
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When solving an equation, we need to find a value of x which makes each side equal each other. We need to remember that 
is equal to and the same as 
. When we solve an equation, if we make a change on one side, we therefore need to make the exact same change on the other side, so that the equation stays equal and true. To illustrate, let's take a numerical equation:
If we subtract 
from each side, the equation still remains equal:
If we now divide each side by 
, the equation still remains equal:
This still holds true even if we have variables in our equation. We can perform the inverse operations to isolate the variable on one side and find out what number it's equal to. To solve our problem then, we need to isolate our 
term. We can do that by subtracting 
from each side, the inverse operation of adding 
:
We now want there to be one 
on the left side. 
is the same thing as 
, so we can get rid of the 6 by performing the inverse operation on both sides, i.e. dividing each side by 
:
is therefore our final answer.
When solving an equation, we need to find a value of x which makes each side equal each other. We need to remember that
If we subtract
If we now divide each side by
This still holds true even if we have variables in our equation. We can perform the inverse operations to isolate the variable on one side and find out what number it's equal to. To solve our problem then, we need to isolate our
We now want there to be one
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Solve for 
.
Solve for
Tap to reveal answer
Start by adding 10 to both sides of the equation.
Then, divide both sides by 
.
Start by adding 10 to both sides of the equation.
Then, divide both sides by
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Solve for t.
Solve for t.
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First start by distributing the 7.
Now, add both sides by 14.
Finally, divide both sides by 7.
First start by distributing the 7.
Now, add both sides by 14.
Finally, divide both sides by 7.
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Solve for 
:
Solve for
Tap to reveal answer
First, add 
to both sides of the equation:
Then, divide both sides by 
:
First, add
Then, divide both sides by
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Dr. Jones charges a $50 flat fee for every patient. He also charges his patients $40 for every 10 minutes that he spends with him. If Mrs. Smith had an appointment that lasted 30 minutes, how much did she have to pay Dr. Jones?
Dr. Jones charges a $50 flat fee for every patient. He also charges his patients $40 for every 10 minutes that he spends with him. If Mrs. Smith had an appointment that lasted 30 minutes, how much did she have to pay Dr. Jones?
Tap to reveal answer
We can express Dr. Jones's rate in a linear equation:
Since Mrs. Smith's appointment lasted 30 minutes, we have 3 10-minute intervals. Then, we can plug in that number into our above equation to find out how much the appointment cost.
We can express Dr. Jones's rate in a linear equation:
Since Mrs. Smith's appointment lasted 30 minutes, we have 3 10-minute intervals. Then, we can plug in that number into our above equation to find out how much the appointment cost.
← Didn't Know|Knew It →
Roman is ordering uniforms for the tennis team. He knows how many people are on the team and how many uniforms come in each box. Which equation can be used to solve for how many boxes Roman should order?
Roman is ordering uniforms for the tennis team. He knows how many people are on the team and how many uniforms come in each box. Which equation can be used to solve for how many boxes
Tap to reveal answer
The total number of uniforms needed equals the number of students divided by the number of uniforms per box.
The total number of uniforms needed equals the number of students divided by the number of uniforms per box.
← Didn't Know|Knew It →
Jimmy had in lunch money for school. Everyday he spends for food and drinks. What is the expression that shows how much money will he have after each day, where is the days, and is the total amount of money left?
Jimmy had
Tap to reveal answer
Jimmy starts off with $60, and spends $3.50 everyday.
This means that he will have $56.50 after day 1, $53 after day 2, and so forth.
Only one equation satisfies this scenario. The rest are irrelevant.
Jimmy starts off with $60, and spends $3.50 everyday.
This means that he will have $56.50 after day 1, $53 after day 2, and so forth.
Only one equation satisfies this scenario. The rest are irrelevant.
← Didn't Know|Knew It →
What is the solution of that satisfies both equations?
What is the solution of
Tap to reveal answer
Reduce the second system by dividing by 3.
Second Equation:
We this by 3.
Then we subtract the first equation from our new equation.
First Equation:
First Equation - Second Equation:
Left Hand Side:
Right Hand Side:
Our result is:
Reduce the second system by dividing by 3.
Second Equation:
Then we subtract the first equation from our new equation.
First Equation:
First Equation - Second Equation:
Left Hand Side:
Right Hand Side:
Our result is:
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What is the solution of for the systems of equations?
What is the solution of
Tap to reveal answer
We add the two systems of equations:
For the Left Hand Side:
For the Right Hand Side:
So our resulting equation is:
Divide both sides by 10:
For the Left Hand Side:
For the Right Hand Side:
Our result is:
We add the two systems of equations:
For the Left Hand Side:
For the Right Hand Side:
So our resulting equation is:
Divide both sides by 10:
For the Left Hand Side:
For the Right Hand Side:
Our result is:
← Didn't Know|Knew It →
What is the solution of for the two systems?
What is the solution of
Tap to reveal answer
We first multiply the second equation by 4.
So our resulting equation is:
Then we subtract the first equation from the second new equation.
Left Hand Side:
Right Hand Side:
Resulting Equation:
We divide both sides by -15
Left Hand Side:
Right Hand Side:
Our result is:
We first multiply the second equation by 4.
So our resulting equation is:
Then we subtract the first equation from the second new equation.
Left Hand Side:
Right Hand Side:
Resulting Equation:
We divide both sides by -15
Left Hand Side:
Right Hand Side:
Our result is:
← Didn't Know|Knew It →