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Advanced Math/How to solve simple equations?
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Question
Hello Scott,
I'm currently having difficulty understanding the following examples of equations.
1. Solve/find x if: 2x + 4 = 10
x = ?
How do simplify my answer to an integer or a fraction?
2. Solve/find x if: 2x + 38 = 8x – 3
x = ?
How do simplify my answer to an integer or a fraction?
What type of equations are they?
May I kindly ask you how do I solve the above examples, please?
Any idea how I should go about to solve the above equations and how can check the answer? Please advise.
Regards,
Craig.
To solve equations, first put the x terms on one side of the equation by addition or subtraction, and put the constants on the other by addition or subtraction.
The variables may be different, but lets assume the variable is x and the constants are A and B.
Once you have Ax = B, then divide both sides by A, and get x = B/A.
1. Solve/find x if: 2x + 4 = 10; There is a constant over with the x, so subtract 4 from each side. This gives 2x + 4 - 4 = 10 - 4 => 2x = 6. Next, divide by 2, getting 2x/2 = 6/2 =>
x = 3. Putting this back in and checking, it is seen that 2(3) + 4 = 6 + 4 = 10, so this is correct.
To really explain this well, take 2x + 4 + 3x - 7 = 3x - 5x + 7 + 11.
Combing terms, on the left there is a 2x and a 3x, and since 2+3 = 5, that is really 5x.
Also on the left, we have a +4 and a -7, so that is 4-7 = -3, so the left is 5x - 3.
On the right, there is a 3x - 5x, and 3-5 = -2, so we have as -2x.
We also have 7+11, and that is 18, so the right is -2x + 18.
This makes the equation 5x - 3 = -2x + 18.
Adding 2x to both sides gives 5x + 2x - 3 = -2x + 2x + 18.
Since 5x + 2x = 7x and -2x + 2x = 0, the equation is 7x - 3 = 18.
Adding 3 to both sides gives 7x - 3 + 3 = 18 + 3.
On the left, -3+3 is 0; on the right, 18 + 3 = 21; this makes it 7x = 21.
Dividing both sides by the multiplier in front of the x gives 7x/7 = 21/7.
That becomes x = 3.
Checking back to the original gives 2(3) + 4 + 3(3) - 7 = 3(3) - 5(3) + 7 + 11.
That works out to 6 + 4 + 9 - 7 = 9 - 15 + 7 + 11.
That left side is 19 - 7 = 12 and the right side is 27 - 15 - 12,
so the answer checks.
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Answers by Expert:
Scott A Wilson
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That method was used and improvements of it were shown.
The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.
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Master of Science at OSU with high honors in mathematics.
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