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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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Here are several examples in which we solve equations without the use
of stick diagrams. Due to the difficulties in typing fractions, the first
examples have been chosen to avoid them.
Example 1: Solve 4x + 10 = 30
Solution Steps:
| Operation |
Equation |
| given |
4x + 10 = 34 |
| add - 10 to both sides |
4x = 24 |
multiply both sides by ¼
(Take ¼ of both sides) |
x = 6 |
Your teachers may give a different way to indicate the operations.
Check: For x =6
| Left Hand Side |
= 4x+10
= 4*6+10
= 24+ 10
= 34 |
|
Right Hand Side |
= 34 |
So for x =6, the Left Hand Side and Right Hand Side have the same
value.
Example 2: Solve 2x +5 = 9 (animated presentation)
Observe how we subtract 5 from both sides
Example 3: Solve 4x - 10 = - 30
Solution Steps:
| Operation |
Equation |
| given |
4x - 10 = -30 |
| add +10 to both sides |
4x = - 40 |
multiply both sides by ¼
(Take ¼ of both sides) |
x = -10 |
Check: For x =6
| Left Hand Side |
= 4x-10
= 4*10 -10
= 40 - 10
= 30 |
|
Right Hand Side |
= 30 |
So for x =10, the Left Hand Side and Right Hand Side have the same
value.
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