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 1.4a:

Answer: x=2

Solution: Multiply both sides by 42, the smallest number that 3, 7, 2, and 21 divides into evenly.

Simplify:

Subtract 21x from both sides of the equation:

Subtract 30 from both sides of the equation:

Divide both sides by 7:

The answer is x=2.

Check the solution by substituting 2 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 the calculator.

• Left Side:
• Right Side:

Since the left side of the original equation equals the right side of the original equation when 2 substituted for x, then x=2 is the correct answer.

You can also check your answer by graphing (left side of the original equation minus the right side of the original equation). The graph will cross the x-axis at x=2.

If you would like to review the solution to problem 1.4b, click on solution

If you would like to go back to the problem page, click on problem.

If you would like to go back to the equation Table of contents, click on Contents.

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