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# Solving Multi-Step Equations

Solving Multi-Step Equations in One Variable for Algebra 1

by

Tweet## Rob Frederick

on 30 August 2012#### Transcript of Solving Multi-Step Equations

Solving Multi-Step Equations Alex belongs to a music club. In this club, students can buy a student discount card for $19.95. This card allows them to buy CD's for $3.95 each. After one year, Alex has spent $63.40. How many CD's did Alex purchase? -19.95 -19.95 3.95c + 19.95 = 63.40 Cost per CD The variable "c" to

represent how many CD's Cost of discount Total Cost Notice the order of operations for this equation: 2.) Divide both sides by 3.95 3.95c + 19.95 = 63.40 ...now...

what does this mean? We were looking for how

many CD's Alex bought with

his 63.40. Looks like 11 (not

a bad deal since they're about 10

dollars each on itunes...)

Remember it's not enough just

to solve, we need to know

what we've found. Notice we still have to have balance! Let's look at some other examples,

then...

Don't forget to copy down the examples for

your notes... THE ASSIGNMENT #24-38, 49-53 pg. 96-97 SOLVE: 10 = 6 - 2x Please don't forget:

Keep your work organized and you have less chance of getting lost or confused.

MARK YOUR ANSWERS! I can't grade them and give you credit if I can't find them... SOLVE: SOLVE: SOLVE: With fractions q - 1 = 3

15 5 5 q - 1 = 3

15 5 5 OR (15) (15) . ( ) (15) (15) q - 1 = 3

15 5 5 (15) (15) (15) With LIke Terms 6x + 3 - 8x = 13 Don't forget to

CHECK YOUR WORK! With Parenthesis 9 = 6 - (x + 2) Distribute! OR x = -5 Bell-Ringer Copy these into your notebook and select the best answers 1.) Which expression always represents an odd number?

A. n + 1

B. 2n + 1

C. n

D. n + 1

2.) Which expression represents the verbal phrase:

"the sum of three times a number and five"?

F. 3(n + 5)

G. 3 + n 5

H. 3n + 5

J. 3 + (n + 5) 2 2 . plus is

1.) First c, would be multiplied by 3.95

2.) Then, 19.95 would be added to the product Using what we know, what can we do to find c? Notice that this is reversing order of operations; this is because we are "undoing" all of the operations on the variable. To solve, we have to work backward: 1.) Subtract 19.95 from both sides 3.95c 43.45 3.95 3.95 c = 11 So, = -6 -6 4 = -2x -2 -2 -2 = 1x OR x = -2 +1

5 +1

5 q

15 = 4

5 q

15 4

5 1 3 q = 4 3 1 q = 12 q

15 1

5 + = 3

5 3 3 q - 3 = 9 +3 +3 q = 12 6x - 8x + 3 = 13 -2x + 3 = 13 -3 -3 -2x 10 -2 -2 x = -5 = 6(-5) + 3 - 8(-5) = 13 -30 + 3 - (-40) = 13 -30 + 3 + 40 = 13 13 = 13 9 = 6 - x - 2 9 = 4 - x -4 -4 5 -x = -1 -1 -5 = x =

Full transcriptrepresent how many CD's Cost of discount Total Cost Notice the order of operations for this equation: 2.) Divide both sides by 3.95 3.95c + 19.95 = 63.40 ...now...

what does this mean? We were looking for how

many CD's Alex bought with

his 63.40. Looks like 11 (not

a bad deal since they're about 10

dollars each on itunes...)

Remember it's not enough just

to solve, we need to know

what we've found. Notice we still have to have balance! Let's look at some other examples,

then...

Don't forget to copy down the examples for

your notes... THE ASSIGNMENT #24-38, 49-53 pg. 96-97 SOLVE: 10 = 6 - 2x Please don't forget:

Keep your work organized and you have less chance of getting lost or confused.

MARK YOUR ANSWERS! I can't grade them and give you credit if I can't find them... SOLVE: SOLVE: SOLVE: With fractions q - 1 = 3

15 5 5 q - 1 = 3

15 5 5 OR (15) (15) . ( ) (15) (15) q - 1 = 3

15 5 5 (15) (15) (15) With LIke Terms 6x + 3 - 8x = 13 Don't forget to

CHECK YOUR WORK! With Parenthesis 9 = 6 - (x + 2) Distribute! OR x = -5 Bell-Ringer Copy these into your notebook and select the best answers 1.) Which expression always represents an odd number?

A. n + 1

B. 2n + 1

C. n

D. n + 1

2.) Which expression represents the verbal phrase:

"the sum of three times a number and five"?

F. 3(n + 5)

G. 3 + n 5

H. 3n + 5

J. 3 + (n + 5) 2 2 . plus is

1.) First c, would be multiplied by 3.95

2.) Then, 19.95 would be added to the product Using what we know, what can we do to find c? Notice that this is reversing order of operations; this is because we are "undoing" all of the operations on the variable. To solve, we have to work backward: 1.) Subtract 19.95 from both sides 3.95c 43.45 3.95 3.95 c = 11 So, = -6 -6 4 = -2x -2 -2 -2 = 1x OR x = -2 +1

5 +1

5 q

15 = 4

5 q

15 4

5 1 3 q = 4 3 1 q = 12 q

15 1

5 + = 3

5 3 3 q - 3 = 9 +3 +3 q = 12 6x - 8x + 3 = 13 -2x + 3 = 13 -3 -3 -2x 10 -2 -2 x = -5 = 6(-5) + 3 - 8(-5) = 13 -30 + 3 - (-40) = 13 -30 + 3 + 40 = 13 13 = 13 9 = 6 - x - 2 9 = 4 - x -4 -4 5 -x = -1 -1 -5 = x =