Name:______Answer Key______
Linear Equations Notes
1. What is an equation?
Students ideas: done independently and share answers. Why do you think that and why?
2. Definition of an equation.
An equation is two expressions set equal to each other
3. Example of an equation.
3 + 7 = 10 Not an equation: 3 > 2
4. Definition of a linear equation.
A linear equation is an equation that is in the form ax + b = c where a, b and c are any value. The value of the unknown variable x is what we are looking for when solving linear equations.
5. Example of a linear equation.
2x + 3 = 0 Not a linear equation: 3 + 7 – 2 = 8
6. Steps to solving a linear equation.
· Simplify the equation by using the distribution property and combining like terms
· Use addition and subtraction properties to get the variable term to one side by itself. What you do to one side do to the other
· Now use multiplication and division properties to isolate the variable ( get x by itself)
· Plug the value you received for the variable (x) back into the original equation to check your answer
Complete the following examples using the steps:
1. 3x +1 = 4
· Simplify the equation
The equation is already simplified: 3x + 1 = 4
· Get the variable term on one side by itself
3x + 1 = 4
Subtract one to both sides
3x = 3
· Isolate the variable
Divide both sides by 3; x = 1
· Check your answer
3(1) + 1 = 4
4=4
2. 10(x -2) + 2 = 6 + 2x
· Simplify the equation
Distribute the 10
Combine like terms
· Get the variable term on one side by itself
10x – 18 = 6 + 2x
Subtract 2x from both sides
Add 18 to both sides
· Isolate the variable
8x = 24
Divide each side by 8
X = 3
· Check your answer
10 (3 – 2) + 2 = 6 + 2 (3)
12 = 12
Name:______Answer Key______
Linear Equations
Use the applet to complete the first five questions. Complete the rest of the worksheet with your partner.
QUESTIONS 1-5 ARE ALL DIFFERENT ANSWERS!!!!
1. Write down the equation you are trying to solve.
2. Visually represent the equation on the scale below.
3. Solve the equation showing all steps.
4. Check your answer.
5. Write down the equation you asked your partner to solve.
6. 2x - 4 + 5 = 37
X = 18
7. 4 * ( 5 – 3x ) + 8 = 52
X = -2
8. 2(3x - 7) + 4 (3 x + 2) = 6 (5 x + 5)
X = -3
9. Together, Greg and Sara bought a total of 14 oranges. If Sara bought 9 oranges, how
many did Greg buy? Use x as your variable to set up the equation, then solve
X = 5
Name: ______ANSWER KEY______
Ticket to Go
Solve and Check your answers!
1. List the steps to solving a linear equation.
Simplify
Get the variable by itself
Isolate
Check
2. 12 ( 3x + 1 ) = 24
X = 1/3
3. 3(1 − 3x) = 2(−4x + 7)
X= -11
4. n + 2 = −14 – n
X = -8
5. Sydney is 21 years old. She is 3 times as old as her little brother. How old is Sydney’s
little brother? Use x as your variable to set up the equation, then solve.
X = 7