(a) What is the logical first step in solving the equation |2x−1|=5? (b) What is the logical first step in solving the inequality |3x+2|≤8?

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(a) What is the logical first step in solving the equation   |2x−1|=5?   (b) What is the logical first step in solving the inequality  |3x+2|≤8?

SchepperJ · Accepted Answer

Step 1  (a) Consider the given equation |2x−1|=5.  In this equation, only absolute value term is on one side of the equation.  Hence, we can use the property of absolute value to obtain two equations.  Thus, |2x−1|=5 is equivalent to 2x−1=5 and 2x−1=−5.  That is, the logical step in solving the equation |2x−1|=5 will be to use the property of absolute value which says |x|=c is equivalent to |x|=±c.  Hence, the given equation |2x−1|=5 is equivalent to 2x−1=5 and 2x−1=−5.  Step 2  (b) Consider the given inequality |3x+2|≤8.  As it is clear from the above table, solution set of inequality can be written as −8≤3x+2≤8.  Once we have written the inequality in this form, we can split and write it in terms of two inequalities 3x+2≥−8 and 3x+2≤8.  The first logical step in solving the inequality |3x+2|≤8 would be to use the properties of absolute value inequalities and obtain the following inequalities.  3x+2≥−8 and 3x+2≤8.

(a) What is the logical first step in solving the equation |2x-1|=5?

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