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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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If you do not follow the use of parameters below, do not worry.
Take peak at Chapters
15 in Three
Skills for Algebra. It will give you a second perspective on solving
linear equations starting with examples simpler than you have mastered in this
site area, but that second perspective also may also help you understand the
following example. It is an example from the end of Chapter 15.
Example 1: Solve ax+b = -cx+d
See Animation below
Find an expression for x which solves the equation
ax+b = -cx+d
Look at the solution before and see if you understand it. If
not, do not worry, the preparation for understanding it is incomplete. If
you do not follow all the steps, you may visit Chapters
8 to 15 in the online book Three
Skills for Algebra. Chapters 15 may be the most useful.
| Operation |
Equation |
| given |
ax+b = -cx+d |
| add -b to both sides |
ax = -cx+d - b |
| add cx to both sides |
ax +ac = d - b |
Apply distributive law in
reverse (factor x) |
(a+c)x = d - b |
Divide both sides by (a+c) if
a+c is non zero. |
|
See if you can check that
satisfies the original equation ax+b = -cx+d.
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