SOLVING LINEAR EQUATIONS

• 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 operation, multiplication and division are completed before addition and subtraction.

LINEAR EQUATIONS - Solve for x in the following equation.

Problem 1.3a:

2 x + 7 = 10 x + 3

Solution:

Subtract 2x from both sides of the equation:

Subtract 3 from both sides of the equation:

Divide both sides by 8:

Check the solution by substituting 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.

• Left side:

• Right side:

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

Solution:

Subtract 3x from both sides of the equation:

Add 4 to both sides of the equation:

Divide both sides by 13:

Check the solution by substituting 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.

• Left side:

• Right side:

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

• Left side: 3 (0.076923) - 3 = - 2.76923

• Right side: 16 (0.076923) - 4 = - 2.76923

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

Solution:

Subtract 3x from both sides of the equation:

Add 17 to both sides of the equation:

Divide both sides by 2:

Check the solution by substituting 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.

• Left Side:

• Right Side:

• Left side: 5 (9.5) - 17 = 30.5

• Right side: 3 (9.5) + 2 = 30.5

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

Solution:

Subtract 8x from both sides of the equation:

Subtract 5 from both sides of the equation:

Divide both sides by 2:

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.

• Left side: 10 (1) + 5 = 15

• Right side: 8 (1) + 7 = 15

Problem 1.3e:

Solution:

Subtract 2x from both sides of the equation:

Add to both sides of the equation:

Divide both sides by 2:

Check the solution by substituting 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.

• Left side:

• Right side:

• Left side:

• Right side:

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