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THE UNKNOWN // FIELD NOTES // WEEK 07

Week 7: Solving multi-step equations

Field Book
25 to 27
Due
Test 5 due
Method
Paper first, every step
One rule is rarely enough. This week the equations take several moves to open, and the order of those moves is the skill: simplify each side, gather the variable on one side, then the two rules finish it.

What you have to be able to do

The procedures

The order of the moves
  1. Simplify each side by itself first: distribute, then collect like terms.
  2. Use rule one to gather the variable terms on one side and the plain numbers on the other.
  3. Use rule two last, to clear the final coefficient.
Variables on both sides
  1. Pick a side for x, usually the side with more of it.
  2. Subtract the smaller x term from both sides.
  3. From there it is a two-step equation you already know.
Checking
  1. Multi-step work multiplies the chances for a sign slip.
  2. Substitute the answer into the original equation, not a middle line.
  3. Both sides must land on the same number.

Worked

WORKED
Solve 5x + 7 − 2x = 22.
Collect: 3x + 7 = 22.
Subtract 7, then divide by 3.
ANSWER: x = 5
WORKED
Solve 4(x − 2) = 2x + 10.
Distribute: 4x − 8 = 2x + 10.
Subtract 2x, add 8: 2x = 18.
ANSWER: x = 9

Terms

TermMeaning
terma piece of an expression separated by plus or minus signs
simplifyrewrite in fewer pieces without changing the value
evaluatefind the number an expression equals

Check yourself

1. Solve: 2x + 9 = 25
2. Solve: 6x − 4 = 3x + 11
3. Solve: 5(x + 1) = 30
reveal answers
x = 8 · x = 5 · x = 5
This page is the summary, not the lesson. The full working, every step of every example, is on the board in class. Come here to remember what the week was about. Go there to learn how it is done.
-- THE UNKNOWN -- week 7, solving multi-step equationsalgebra 1 · oda