SOLVING LINEAR EQUATIONS

Recall the following:

• A linear equation is a polynomial of degree 1.

• In order to solve for the unknown variable, you must isolate the variable

• In the order of operations, multiplication and division are completed before addition and subtraction.

• Problem 1.1a: x + 7 = 3

  
  Answer: x = - 4

  
  Solution: Subtract 7 from both sides of the equation.

  

  which gives:

  x = - 4

  
  Check: Substitute -4 for x in the original equation. If, after the substitution, the left side equals the right side, your answer is correct. ( -4 ) + 7 = 3 Your answer is correct.

Problem 1.1b: x - 3 = 4

Answer: x = 7

Solution: Add 3 to both sides of the equation

which gives:

x = 7

Check: Substitute 7 for x in the original equation. If, after the substitution, the left side equals the right side, your answer is correct. ( 7 ) - 3 = 4 . Your answer is correct.

Problem 1.1c: x - 17 = 3

Answer: x = 20

Solution: Add 17 to both sides of the equation.

which gives:

x = 20

Check: Substitute 20 for x in the original equation. If, after the substitution, the left side equals the right side, your answer is correct. (20) - 17 = 3 . Your answer is correct.

Problem 1.1d: x + 5 = 8

Answer: x = 3

Solution: Subtract 5 from both sides of the equation.

which gives:

x = 3

Check: Substitute 3 for x in the original equation. If, after the substitution, the left side equals the right side, your answer is correct. (3) + 5 = 8. Your answer is correct.

Problem 1.1e:

Answer:

Solution: Add to both sides of the equation.

which gives:

Add the fractions.

Check: Substitute for x in the original equation. If, after the substitution, the left side equals the right side, your answer is correct. .

Your answer is correct.

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