Solving Linear Equations

1-step Equations: + and – 2/27/13In elementary school, you solved

equations that looked like this:

In Algebra, we just use a variable instead of the box!

We could rewrite the same equation like this: x + 3 = 5

To solve:Need to get x by itself.We must “undo” whatever has been

done to the variable.Do the same to BOTH SIDES of the =

sign!Answer should be: x = some number.

Equations Have to Balance!Both sides of the = sign must “weigh”

the same!When you change one side, do the same

to the other side, so it stays balanced! x + 3 = 7

Examples:Solve each equation. Check your

answers! x + 3 = -7 m – 6 = 8

4 + a = -3

-8 + y = 7

24 = 12 + t

-17 = x – 2

You Try!Solve each equation. Check your

answers! x – 9 = -6 16 + n = 10

1-step Equations: × and ÷ 3/11/13Just 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 means

divide!Example: says x divided by 3!

Examples:Solve each equation:2x = 8

12 = -3b

You Try!Solve each 1-step equation. -4a = 16

Basic 2-Step Equations 3/13/13A 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 firstMultiply/Divide last

Examples:4x + 7 = 27 – 6 – 2y = 10

5 = 7r - 2 -4 = 2 - m

You Try!Solve each equation. Check your

answers!-3x + 7 = 16 -8 = 2a + 2

Multi-Step Equations 3/18/13Multi-step equations have ( ).To solve:

Distribute first!!Then, solve like a 2-step equation!

Example: 4(-x + 4) = 12

Examples:3(– 6 + 3x) = 18

30 = -5(6n + 6)

10 (1 + 3b) = -20

-2 = -(n – 8)

Your Try!-6(1 – 5v) = 54

2 Variables- Same Side 3/21/13Some equations have variables in more

than one place.When variables are on the same side

of the = sign:First, Combine Like Terms

Like terms may NOT cross the = sign!Then, solve like a 2-step

Examples:2x + 3x + 1 = 36

3 + 6x – 2x = -5

-26 = -7x + 6 + 3x

You Try!Solve for x.8x – 3x + 7 = 17

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 from both sides.

2. Solve like a 2-step equation.

Examples9 – 7x = -5x – 7

-3x – 7 = 2x – 13

You Try!-3x + 9 = 44 + 4x