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Solving Linear
Equations
(Feb 14, 2005)
with & then without stick diagrams plus
solving word problems; and solving systems: - essentially one
unknown, essentially triangular & general
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Solve 4x + 10 = 30
Solve 3x -4 = -11
(¼)x = x - 9
Solve ax+b = cx + d
Read them in order
(i) x + 20 = 29 WS
(ii) 2x + 6 = 24 WS
(iii) 3x + 10 = 32 WS
(iv) 5a + 16 = 3a+ 24 WS
(v) (½)x + 8 = 24½ WS
(vi) (¾)a + 16 = (¼)a+ 24 WS
(vii) (¾)q + 17 = 32 WS
(viii) 13 =[2/3]x +7 twice WS
(5/6)q + 8+(5/6) = 14 + (2/3) WS
Proper Use of Equal Sign
Up
Solve 4x + 10 = 30
Solve 3x -4 = -11
(¼)x = x - 9
Solve ax+b = cx + d
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Equations with Fractional Coefficients.
Example 1: Solve (¼)x = x - 9
Solution Steps:
| Operation |
Equation |
| given |
(¼)x = x - 9 |
| add - x to both sides |
- (¾)x = - 9 |
| multiply both sides by -1 |
(¾)x = 9 |
| Next multiply both sides by |
1
3 |
|
(¼)x = 3 |
| multiply both sides by 4 |
x =12 |
| Note instead of multiply by -1, then |
1
3 |
and then 4, |
| we could have multiplied by their product |
-4
3 |
in a single step |
How many step you take, depends on what you see. And after you written a
solution and checked it, you may see a simpler or quicker way. You may if
your pride insists, rewrite the solution in the quicker way. Sometimes I
do and sometimes I don't.
Check: For x =12
| Left Hand Side |
= (¼)x
=(¼)12
= 3 |
|
Right Hand Side |
= x -9
=12 -9
= 3 as well. |
So for x =12, the Left Hand Side and Right Hand Side of the equation (¼)x =
x - 9 have the same value 3.
Example 2: (2/3)x + 4 = -(1¼) x+8 Animated Solution
Example 3: (2/3)x + 5/8 = -¾ x - 3.375 Animated Solution
Example 4. -¾ x - (5/6) = (5/8)x + 7/12 Animated Solution
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