SOLVING LINEAR EQUATIONS

Read the following:


LINEAR EQUATIONS - Solve for x in the following equation.

Problem 1.3a:

2 x + 7 = 10 x + 3

Answer: tex2html_wrap_inline275

Solution:

Subtract 2x from both sides of the equation:

displaymath241




Subtract 3 from both sides of the equation:

displaymath242




Divide both sides by 8:

displaymath243




The answer is tex2html_wrap_inline279




Check the solution by substituting tex2html_wrap_inline275 in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.


Problem: 1.3b:
3 x - 3 = 16 x - 4

Answer: tex2html_wrap_inline291

Solution:

Subtract 3x from both sides of the equation:

displaymath244




Add 4 to both sides of the equation:

displaymath245




Divide both sides by 13:

displaymath246




The answer is tex2html_wrap_inline295




Check the solution by substituting tex2html_wrap_inline291 in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.




You can also check your answer with a calculator: x = 0.076923


Problem 1.3c:
5 x - 17 = 3 x + 2

Answer: tex2html_wrap_inline313

Solution:

Subtract 3x from both sides of the equation:

displaymath247




Add 17 to both sides of the equation:

displaymath248




Divide both sides by 2:

displaymath249




The answer is tex2html_wrap_inline317




Check the solution by substituting tex2html_wrap_inline313 in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.




You can also check your answer with the calculator where x=9.5





Problem 1.3d:
10 x + 5 = 8 x + 7

Answer:x=1.

Solution:

Subtract 8x from both sides of the equation:

displaymath250




Subtract 5 from both sides of the equation:

displaymath251




Divide both sides by 2:

displaymath252




The answer is x = 1




Check the solution by substituting 1 in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.





Problem 1.3e:
tex2html_wrap_inline339

Answer: tex2html_wrap_inline341

Solution:

Subtract 2x from both sides of the equation:

displaymath253




Add tex2html_wrap_inline345 to both sides of the equation:

displaymath254




Divide both sides by 2:

displaymath255




The answer is tex2html_wrap_inline347




Check the solution by substituting tex2html_wrap_inline341 in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.




You can also check the answer with your calculator, and x=0.763889


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[Algebra] [Trigonometry]
[Geometry] [Differential Equations]
[Calculus] [Comples Variables] [Matrix Algebra]

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Author:Nancy Marcus

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