Lesson 1 Solving of Linear Equations
Example 1a
5x - 10 = 2(x-4) First you must multiply the x - 4 by 2 before you begin your steps of solving.
5x - 10 = 2x - 8 Now begin solving: Subtract 2xfrom both sides.
5x -10 -2x= 2x - 8 - 2x This is how we move the x term to the left side of the equation.
3x - 10 = - 8 Now ADD 10 to both sides.
Did you notice that the 10 is negative and that it is on the left side of the equation? This is how we move the -10 term to the right side of the equation.
3x - 10 + 10 = -8 + 10
3x = 2 To finish with 1x instead of 3x, divide by 3 or multiply by 1/3.
3x/3 = 2/3 divide by 3 or multiply by 1/3.
1x = 2/3 We always want to finish with 1x.
Example 1b
3(x-8) = 2x - 4 +3x LOOK ; I simplified each side before solving.
3x - 24 = 5x - 4 do you see where the 5x came from?
Now subtract 5x from both sides
3x -5x -24 = 5x -5x -4
-2x -24 = - 4
-2x -24 + 24 = - 4 +24
-2x = 20 Now divide both sides by the -2.
1x = -10
Sometimes you may have -x at the end of the problem, -x = 10 is not a finished problem. So please know that it is ok to get -x = 10 but that you need one more step: x= -10.
We always finish with what 1x or x equals.
If a negative x = positive 10 then isn't it logical
that positive x = negative 10?
If we solve an equation for x and we have -x = -14 at the end of a problem then that means +x = +14. Be sure to give that as you final answer; x=14. (We divided both sides by -1.)
Please stop and do
ASSIGNMENT 1A then continue below.*********************
Example 1c
2x/3 - x/6 = 1/2 This is x/6 subtracted from 2x/3 to equal 1/2.
Please not that 2x/3 is 2x/3 and means 2 thirds of x.
We need to subtract the 1x/6 from the 2x/3 that means LCD is needed. The LCD is 6 so the 2x/3 becomes 4x/6. (2/3 is same as 4/6)
4x/6 - 1x/6 = 1/2
3x/6 = 1/2
To find what 1x is instead of the 3 sixth x, we multiply both sides by 6. HOPE you know that 6 times 3 sixth equals 3 the whole number.
Right? so 6 times (3sixth x) is 3x.
(6)3x/6 = (6)(1/2) Multiply both sides by 6.
3x = 3
x= 1
Example 1d
2x/3 + 6 = 4 This is the sumof 2 thirds of a number and 6 to = 4.
Let's begin solving by subtracting 6.
AND remember , a little arithmetic lesson thrown in here,
(3 halves) times (2 thirds)x is 6x/6 =1x. We MUST finish with 1x on left side.
And (3 halves) times (-2) is-6/2 = -3.
1x = -3 or simply x = -3
NOW do ASSIGNMENT 1CDthen continue below.*********************
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Try this out of our classroom example. It is cool.
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Example 1e
Example 1f
I used blue and red text below; be sure you can see it.
(3x-2)/12 - x/9 = 2x OR
All terms must be multiplied by the LCM,
even if they are not fractional.
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1. LCM for the denominators 12 and 9 is 36. Hope you know that 36 is the smallest number that both12 and 9 divide into evenly.
1. Multiply all terms by the 36.
36*(3x - 2)
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-
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36*x
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=
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36*2x
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12
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9
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2. Divide the 36 by the denominators.
BE SURE YOU are writing this in your notebook. COPY all of these steps.
3*(3x - 2)
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-
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4*x
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=
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36*2x
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1
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1
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3. Now multiply the numerators. And yes all the denominators should be 1 now and thus do not have to be written.
9x - 6 - 4x = 72x Again, be sure you understand the simplifying.
5x - 6 = 72x
-6 = 67x Note the x is on the right side. We divide by the 67.
-6/67 = x or x = - 6/67
You really should write each of the example problems down on your paper and see if you can solve them yourself. Then come back and check them.
Just reading math is not going to get it, unless you have a photogenic mind and an exceptional long term memory.
Do Assignment 1EF .
then return here to click the Lesson Completion Button below. You must do that to continue to the next lesson.
LESSON COMPLETION BUTTON