1. Warm up

2. 8.EE-7. Solve linear equations in one variable.
Standard(s):
8.EE-7. Solve linear equations in one variable.
I can solve any linear equation with rational numbers.
I can solve any linear equation with a variable on both sides.
Designed by Skip Tyler, Varina High School

3. 1) Solve. 3x + 2 = 4x - 1
You need to get the variables on one side of the equation. It does not matter which variable you move. Try to move the one that will keep your variable positive.

4. 1) Solve 3x + 2 = 4x - 1 - 3x - 3x 2 = x - 1 + 1 + 1 3 = x
3 = x
3(3) + 2 = 4(3) - 1
9 + 2 =
Draw “the street”
Determine which side will be the “house of variables” and the “house of constants”.
Subtract 3x from both sides
Simplify
Add 1 to both sides
Check your answer

5. 2) Solve 8y - 9 = -3y + 2 + 3y + 3y 11y – 9 = 2 + 9 + 9 11y = 11 11 11
11y =
y = 1
8(1) - 9 = -3(1) + 2
Draw “the street”
Add 3y to both sides
Simplify
Add 9 to both sides
Divide both sides by 11
Check your answer

6. What is the value of x if 3 - 4x = 18 + x?-3 3
Answer Now

7. 3) Solve 4 = 7x - 3x 4 = 4x 4 4 1 = x 4 = 7(1) - 3(1)
1 = x
4 = 7(1) - 3(1)
Draw “the street”
– Notice the variables are on the same side!
Combine like terms
Divide both sides by 4
Simplify
Check your answer

8. 4) Solve -7(x - 3) = -7 -7x + 21 = -7 - 21 - 21 -7x = -28 -7 -7 x = 4
-7x = -28
x = 4
-7(4 - 3) = -7
-7(1) = -7
Draw “the street”
Distribute
Subtract 21 from both sides
Simplify
Divide both sides by -7
Check your answer

9. What is the value of x if 3(x + 4) = 2(x - 1)?
-14
-13 13 14
Answer Now

10. 5) Solve 3 - 2x = 4x – 6 + 2x +2x 3 = 6x – 6 + 6 + 6 9 = 6x 6 6
Draw “the street”
Clear the fraction – multiply each term by the LCD
Simplify
Add 2x to both sides
Add 6 to both sides
Divide both sides by 6
Check your answer
3 - 2x = 4x – 6
+ 2x +2x
= 6x – 6
= 6x
or 1.5 = x

12. 3 types of linear equation solutions

13. -2x -2x 5 = -3 This is never true! No solutions
Special Case # ) 2x + 5 = 2x - 3
-2x x
5 = -3
This is never true!
No solutions
Draw “the street”
Subtract 2x from both sides
Simplify

15. Infinite solutions or identity
Special Case # ) 3(x + 1) - 5 = 3x - 2
3x + 3 – 5 = 3x - 2
3x - 2 = 3x – 2
-3x x
-2 = -2
This is always true!
Infinite solutions or identity
Draw “the street”
Distribute
Combine like terms
Subtract 3x from both sides
Simplify

17. What is the value of x if -3 + 12x = 12x - 3?4
No solutions
Infinite solutions
Answer Now

18. Challenge! What is the value of x if -8(x + 1) + 3(x - 2) = -3x + 2?-2 2 8
Answer Now