LESSON - Solving Linear Equations

Solving Linear Equations With a Single Variable

GOAL: AN INTERACTIVE ONLINE LESSON
During this lesson you are asked to so participate in some activities and solve some problems.
You ought to take this exercise VERY SERIOUS!
For each completed activity you'll earn points - this exercise is not a typical math test but once you are actively involved you will master the concept.

Linear Equations

A linear equation is an equation that consists of one single variable.
Linear equations do not include variables raised to a power or square roots of variables.

Multiple Choice

Which equation below represent a linear equation?

• $$2x^2+3x-12=0$$

• $$3x-6=8$$

• $$3x-4=6y+3$$

• $$3x\left(x-1\right)=2$$

• $$\sqrt[]{x}+2=0$$

Let's crosscheck your previous knowledge

Let's see whether you remember distributive, associative and commutative.

NOTE: you will earn points along the way!

Fill in the Blank

2+4=4+2 represents what property of numbers?

Fill in the Blank

2+(x+2)=(2+x)+2 represents what property?

Fill in the Blank

2(3+4)=2x3+2x4 represents what property?

Multiple Choice

Which of the following equations would be equivalent to  $$4x+3=8\left(x+4\right)$$  after the Distributive Property has been applied?

• $$4x+7=12$$  

• $$4x+3=8x+32$$  

• $$4x+3=8+4x$$  

Multiple Choice

Which of the following equations would be equal to  $$5\left(4-y\right)=45-6y$$ after the Distributive Property has been applied? 

• $$20-y=39y$$  

• $$4-5y=45-6y$$  

• $$20-5y=45-6y$$  

Match

Match the following

• 2(2x+4)

• 4x-4

• (2x+3)+2

• 5x+(5+3)

• 8+2x

4x+8

-4+4x

2x+(3+2)

(5x+5)+3

2x+8

• 4x+8

• -4+4x

• 2x+(3+2)

• (5x+5)+3

• 2x+8

Let's take some notes

Step 1: Apply the Distributive Property if possible

If an equation has parentheses, you should be able to simplify it using the Distributive Property. The Distributive Property states that you can distribute multiplication across addition or subtraction. Some examples are shown to the right.

Step 2: Combine like terms on each side of the equation if necessary

Like terms can be combined on each side of the equation to simplify. Remember like terms are terms that either have the same variable or no variable at all.

Step 3: Simplify by using properties of equality

When you have variable terms on both sides of the equation, you can simplify by either adding or subtracting the same amount from both sides. You want to simplify the equation so that you have one variable term left on one side and a constant on the other.

Step 4: Isolate the variable to find its value

If you are able to get the variable on one side of the equation by itself, you will know its value. This is done by performing the opposite of what is being done to the variable and usually involves multiplication or division.

These steps can be used to solve ANY linear equation with a single variable.

Good luck with solving equations!

Open Ended

Write down the four steps needed to solve a linear equation. Remember - for each completed exercise you'll earn points

Now we will solve an equation from start to finish using all four steps

We will perform one step at a time

Steps for solving a linear equation with a single variable

1) Apply the Distributive Property if possible

2) Combine like terms on each side of the equation if necessary

3) Simplify by using properties of equality so that you're left with a variable term on one side and a constant on the other

4) Isolate the variable to find it's value

Let's crosscheck whether you understand the steps

Multiple Choice

Which of the following equations would be equal to $$12x+6=9x+15$$ after simplifying by using properties of equality?

• $$3x=21$$  

• $$21x=21$$  

• $$3x=9$$  

Multiple Choice

Which of the following equations would be equivalent to $$4x+6+8x=2x+18$$  after like terms are combined? Remember you can only combine like terms on one side of the equals sign.

• $$12x+6=2x+18$$  

• $$14x=12$$  

• $$10x+8=2x+18$$  

Multiple Choice

Which of the following equations would be equivalent to $$9y-14=5y-12-6$$  after like terms are combined? Remember you can only combine like terms on one side of the equals sign, and anything being subtracted must be treated as a negative value.

• $$14y-14=-18$$  

• $$9y-14=5y-18$$  

• $$9y-14=-7y-6$$  

Multiple Choice

Solve the equation $$3y=27$$ by isolating the variable.

• $$y=3$$  

• $$y=9$$  

• $$y=87$$  

Let's discuss another example:

Dropdown

The first thing when solving 2(x+3)=8 equals​

Select answer

; thereafter​

Select answer

; followed by ​

Select answer

Reorder

Write down the steps in the correct order when solving the following equation: 3(x + 2) = 5x + 8

• 3x+6=5x+8

• 6-8=5x-3x

• -2=2x

• -2/2=x

• -1=x

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Draw

Solve for x in the equation.

4(x - 3) = 40

Draw

Solve for x in the equation.

2(4x - 3 ) = 2

Let's solve:4(x+6)+2x=12x-18

Multiple Choice

Step 1: Simplify the equation $$4\left(x+6\right)+2x=12x-18$$ by applying the Distributive Property. We are only performing one step at a time.

• $$4x+8x=12x-18$$  

• $$4x+24+2x=12x-18$$   

• $$8x+6=12x-18$$  

Multiple Choice

Step 2: Simplify the equation $$4x+24+2x=12x-18$$ by combining like terms. We are only performing one step at a time. 

• $$6x+24=12x-18$$  

• $$30x=12x-18$$  

• $$6x+24=-6x$$  

Multiple Choice

Step 3: Simplify the equation $$6x+24=12x-18$$ by using properties of equality. Remember to cancel terms by either adding or subtracting the same thing from both sides. 

• $$6=6x$$  

• $$18x=6$$  

• $$42=6x$$  

Multiple Choice

Step 4: Solve the equation $$42=6x$$ by isolating the variable. Remember to perform the opposite of what is being done to the variable on both sides. 

• $$x=12$$  

• $$x=7$$  

• $$x=252$$  

Here is a recap of the steps we took to solve this problem

Step 1: Apply the Distributive Property

Step 2: Combine Like Terms

Step 3: Simplify using properties of equality

Step 4: Isolate the variable

linear equations with fractions

It is important to watch the following video; thereafter you get two linear equations involving fractions for you to solve!
Let's earn points!!

Multiple Choice

solve: $$2\left(x+5\right)=\frac{1}{2}\left(x-4\right)$$

• -8

• 6

• -6

• 8

Multiple Choice

Solve $$\frac{5}{2}\left(6x-8\right)=\frac{1}{3}\left(9x+12\right)$$

• -3

• -2

• 2

• 3

Video Response

solve the following equation $$\frac{1}{4}\left(x+1\right)=\frac{x}{2}+3$$ on a piece of paper and record it (max 1 minute)

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Audio Response

Did you enjoy this interactive full online lesson in 'solving linear equation'?

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