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# Linear equations

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### Linear equations

1. 1. 1-step Equations: + and – 2/27/13In elementary school, you solvedequations that looked like this:In Algebra, we just use a variableinstead of the box!We could rewrite the same equationlike this: x + 3 = 5
2. 2. To solve:Need to get x by itself.We must “undo” whatever has been doneto the variable.Do the same to BOTH SIDES of the = sign!Answer should be: x = some number.
3. 3. Equations Have to Balance!Both sides of the = sign must “weigh” thesame!When you change one side, do the sameto the other side, so it stays balanced!x + 3 = 7
4. 4. Examples:Solve each equation. Check your answers!x + 3 = -7 m – 6 = 8
5. 5. 4 + a = -3-8 + y = 7
6. 6. 24 = 12 + t-17 = x – 2
7. 7. You Try!Solve each equation. Check your answers!x – 9 = -6 16 + n = 10
8. 8. 1-step Equations: × and ÷ 3/11/13Just like with adding and subtracting,we need to “undo” what is done to x.Use division to “undo” multiplication.Use multiplication to “undo” division.Remember: A fraction bar meansdivide!Example: says x divided by 3!
9. 9. Examples:Solve each equation:2x = 812 = -3b
10. 10. You Try!Solve each 1-step equation.-4a = 16
11. 11. Basic 2-Step Equations 3/13/13A lot like 1-step equations!Goal: Get x by itself!Need to “undo” what is done to x.Always do the same thing to BOTH SIDES!Use Order of Operations backwards:Add/Subtract firstMultiply/Divide last
12. 12. Examples:4x + 7 = 27 – 6 – 2y = 10
13. 13. 5 = 7r - 2 -4 = 2 - m
14. 14. You Try!Solve each equation. Check your answers!-3x + 7 = 16 -8 = 2a + 2
15. 15. Multi-Step Equations 3/18/13Multi-step equations have ( ).To solve:Distribute first!!Then, solve like a 2-step equation!Example: 4(-x + 4) = 12
16. 16. Examples:3(– 6 + 3x) = 1830 = -5(6n + 6)
17. 17. 10 (1 + 3b) = -20-2 = -(n – 8)
18. 18. Your Try!-6(1 – 5v) = 54
19. 19. 2 Variables- Same Side 3/21/13Some equations have variables in morethan one place.When variables are on the same side ofthe = sign:First, Combine Like Terms Like terms may NOT cross the = sign!Then, solve like a 2-step
20. 20. Examples:2x + 3x + 1 = 36
21. 21. 3 + 6x – 2x = -5
22. 22. -26 = -7x + 6 + 3x
23. 23. You Try!Solve for x.8x – 3x + 7 = 17
24. 24. Variables on Both Sides 3/22/13To solve equations like this:2x – 4 = 2 + 5x1. Get variables together on the left. Add or subtract right side x term fromboth sides.2. Solve like a 2-step equation.
25. 25. Examples9 – 7x = -5x – 7
26. 26. -3x – 7 = 2x – 13
27. 27. You Try!-3x + 9 = 44 + 4x