The case work starts here. An equation is a balance, and there are exactly two legal moves: add or subtract the same thing on both sides, or multiply or divide both sides by the same nonzero number. The rest of the year is those two rules, applied in the right order.
What you have to be able to do
Solve one-step equations with the two rules
Keep an equation balanced through every move
Check a solution by substitution
The procedures
Rule one
Add the same quantity to both sides, or subtract it from both sides.
Use it to move added or subtracted numbers away from the variable.
The balance holds because both sides changed together.
Rule two
Multiply both sides by the same nonzero number, or divide both sides by it.
Use it to clear a coefficient or a denominator.
Never multiply or divide by zero; zero destroys the case.
Checking
A solution closes the case only if it makes the equation true.
Substitute it back and compute both sides.
If the sides disagree, the case is still open: rework it.
Worked
WORKED
Solve x − 9 = 15. Add 9 to both sides. Check: 24 − 9 is 15. ANSWER: x = 24
WORKED
Solve 4x = 28. Divide both sides by 4. Check: 4 × 7 is 28. ANSWER: x = 7
Terms
Term
Meaning
equation
a statement that two expressions are equal
solution
the value that closes the case: it makes the equation true
inverse operation
the operation that undoes another
Check yourself
1. Solve: x + 11 = 4
2. Solve: x6 = 5
3. Solve: 3x = −21
reveal answers
x = −7 · x = 30 · x = −7
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 6, equations begin: the two rulesalgebra 1 · oda