# Problem of the Week

## Updated at Aug 8, 2022 9:57 AM

How can we solve the equation $$\frac{{(4(y-3))}^{2}}{5}=\frac{16}{5}$$?

Below is the solution.

$\frac{{(4(y-3))}^{2}}{5}=\frac{16}{5}$

 1 Use Multiplication Distributive Property: $${(xy)}^{a}={x}^{a}{y}^{a}$$.$\frac{{4}^{2}{(y-3)}^{2}}{5}=\frac{16}{5}$2 Simplify  $${4}^{2}$$  to  $$16$$.$\frac{16{(y-3)}^{2}}{5}=\frac{16}{5}$3 Multiply both sides by $$5$$.$16{(y-3)}^{2}=\frac{16}{5}\times 5$4 Cancel $$5$$.$16{(y-3)}^{2}=16$5 Divide both sides by $$16$$.${(y-3)}^{2}=1$6 Take the square root of both sides.$y-3=\pm \sqrt{1}$7 Simplify  $$\sqrt{1}$$  to  $$1$$.$y-3=\pm 1$8 Break down the problem into these 2 equations.$y-3=1$$y-3=-1$9 Solve the 1st equation: $$y-3=1$$.1 Add $$3$$ to both sides.$y=1+3$2 Simplify  $$1+3$$  to  $$4$$.$y=4$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$y=4$10 Solve the 2nd equation: $$y-3=-1$$.1 Add $$3$$ to both sides.$y=-1+3$2 Simplify  $$-1+3$$  to  $$2$$.$y=2$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$y=2$11 Collect all solutions.$y=4,2$Doney=4,2