Question

Find the solution set of |5y - 3| - 6 = 3.

Answer 1

Answer:

Using ∣x∣>a⇔x<−a or x>a, we get

∣2x−3∣>1⇒2x−3<−1 or 2x−3>1

⇒x<1 or x>2⇒x∈(−∞,1)∪(2,∞)

Answer 2

Answer:

The solution set is $y=\{-\frac{6}{5}, \frac{12}{5}\}$

Step-by-step explanation:

Given the absolute value equation,

                    $\big|5y - 3 \big| - 6 = 3$

For a positive case,

                    $\big|5y - 3 \big| - 6 = 3\implies \big(5y - 3 \big) = 3+6$

                                               $\implies 5y =9+3 \implies 5y =12$

                                               $\implies y =\frac{12}{5}$

For a negative case,

                    $\big|5y - 3 \big| - 6 = 3\implies \big-(5y - 3 \big) = 3+6$

                                               $\implies -5y + 3 = 3+6$

                                               $\implies-5y =6$

                                               $\implies y =-\frac{6}{5}$

Therefore the solution set is $y=\{-\frac{6}{5}, \frac{12}{5}\}$