Download How many potato chips are in the bag if the bag plus five more

One-Step Linear Equations
An equation is a mathematical sentence that contains an equal (=) sign and states that two
expressions are equal. An equation can be solved.
Examples of equations: 12 + 8 = 20 and 25 x 3 = 75
When we are working with equations, we need to know the term variable. A variable is a
symbol, or place holder. It is usually a letter used to represent an unknown value.
Examples of variables:
a + 5 = 15
5y = 25
22 – z = 12
The letters a, y, and z are all used as variables in the equations above.
A term is a number, variable, product, or quotient in an expression of sums and/or differences.
Therefore, if we remove all the operation signs in the equation, the terms are what are left.
For example, in 2x – 6, there are two terms: 2x and 6
We know that an equation is a mathematical sentence that contains an equal (=) sign.
In an equation, the expressions on either side of the equals sign are equal.
The scale above is balanced. Just like an equation, both sides of the scale are equal. If,
however, we remove two cubes from the left side of the scale, the scale will be out of balance.
The left side will be lighter than the right side. What could we do to the right side of the scale
to make it balanced once again?
Yes, we remove two blocks from the
right side to make both sides balanced.
It is important to remember that for a scale or an equation to remain balanced or
equal, anything that is done to one side must be done to the other side.
One-Step Linear Equations
Example:
x+2 = 4
–2 =–2
x+0 =
2
x =
2
Step 1: Subtract! It is the inverse or opposite operation of addition.
Remember to subtract 2 from both sides to keep things balanced!
Step 2: Simplify!
Check our answer:
x+2=4
Substitute 2 for x
2+2=4
That works!
One-Step Equations
A one-step equation is an equation that only requires one operation to solve. We can solve
one-step equations by using inverse operations. As we know, the inverse of addition is
subtraction and the inverse of multiplication is division. In most simple problems, we can use
the inverse operations to solve the equations.
Example:
Let’s look at an addition problem. Remember we will use subtraction to solve the problem
since subtraction is the inverse of addition.
x+2=8
Think: 8 – 2 = 6
Even though the operation in the problem is addition, we can use subtraction to solve it.
x is equal to 6.
Check our answer: x + 2 = 8
Substitute 6 for x
Example:
6 + 2 = 8 That works!
One-Step Linear Equations
Let’s look at a subtraction problem. Remember we will use addition to solve the problem since
addition is the inverse of subtraction.
d–3=4
Think: 3 + 4
=7
Even though the operation in the problem is subtraction, we can use addition to solve it.
Check our answer: d – 3 = 4
Substitute 7 for d
7 – 3 = 4 That works!
Open Sentence
Let’s review! An open sentence is a mathematical sentence that contains a variable. As we
know, a variable is a letter that stands for the value that we are looking for. It also contains
an equal (=) sign.
Example:
How many potato chips are in the bag if the bag plus five more equals 43 potato chips? The
variable b stands for the number of chips in the bag.
b + 5 = 43
As we know, a variable is the letter that stands for the value that we are looking for. In the
potato chip problem, we are looking for b, the number of chips in the bag.
b + 5 = 43
b - 5 = 43 – 5
Step 1: Subtract! It is the inverse or opposite operation of addition.
Remember to subtract 5 from both sides to keep things balanced!
b + 0 = 38
b = 38
Step 2: Simplify!
Check our answer: b + 5 = 43
Substitute 38 for b
Example:
38 + 5 = 43 That works!
One-Step Linear Equations
Jack’s dog weighs twice as much as his cat. If his dog weighs 28 pounds, how much does his
cat weigh?
1. Let’s make p stand for the weight of the cat.
2. Put the rest of the problem into a mathematical sentence to include an equal sign (=).
2p = 28
See how the 2 is right next to the variable p? That means it is 2 times the variable.
Look back at the problem. It says Jack’s dog weighs twice as much as his cat. Twice as much
means the same as 2 times the variable.
2p = 28
2 ÷ 2p = 28 ÷2
Step 1: Divide! It is the inverse operation of multiplication.
Remember! Divide 2 from both sides to keep things balanced!
1p = 14
P = 14
Step 2: Simplify!
Check our answer: 2p = 28
Substitute 14 for p
2(14) = 28
28 = 28 That works!
As we have learned, there are different ways to write a multiplication problem. Notice in this
multiplication problem, we wrote 2p meaning 2 x p or 2 · p. There doesn’t have to be a
multiplication sign (x or ·) when a variable and a number are placed side by side.
It really does help to take problems with numbers and turn them into mathematical sentences
in order to solve them!
PRACTICE!
One-Step Linear Equations
1. Tickets to the concert cost $12. Which of the following sentences shows the
cost (c) of 8 tickets?

12c = 8

12 x 8 = c


8c = 12
12 + 8 = c
Write a story problem for the following open sentences:
2.
c
= 12
3
3.
n + 3 = 10