SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:

• if and only if

• if and only if a+b=3 or a+b=-3

• Step 1:Isolate the absolute value expression.

• Step 2:Set the quantity inside the absolute value notation equal to + and - the quantity on the other side of the equation.

• Step 3:Solve for the unknown in both equations.

• Step 4:Check your answer analytically or graphically.

Solve for x in the following equation.

Solve for x in the following equation.

Problem 1c:

Answer: No solution.

Note that the absolute value of an expression can never equal a negative number. There is no solution.

Suppose you did not make this observation and went ahead with the solution. You will catch it in the check because the solutions will not check.

Step 1: Set the quantity within the absolute value notation to

Step 2: Solve for x in the equation 10x - 3 = - 7 :

Solve for x in the equation 10x - 3 = 7:

The indicated answers are 1 and . These answers may not be solutions to the original equation; you must verify the solutions.

Step 3:Check the solutions.

Check the answer x=1 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:

• Right Side:

Since the left side of the original equation does ot equal the right side of the original equation after we substituted the value 1 for x, x=1 is not a solution.

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:

Since the left side of the original equation does ot equal the right side of the original equation after we substituted the value for x, is not a solution.

There are no solutions.

You can also check your answer by graphing (the left side of the original equation minus the right side of the original equation). You will note that the there are no intercepts on the graph. There are no solutions.

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