Core Connections Algebra 2, 2013
CC
Core Connections Algebra 2, 2013 View details
Chapter Closure

Exercise 181 Page 117

a To solve the given literal equation for y, we will use the Properties of Equality to apply inverse operations on the equation. Remember, only like terms can be combined.
4-2(x+y)=9
-2(x+y)=5
x+y=5/-2
x+y=-5/2
y=- x-5/2
b To solve the given literal equation for y, we will use the Properties of Equality to apply inverse operations on the equation. Remember, only like terms can be combined.
x=2(y-1)^2+2
x-2=2(y-1)^2
x-2/2=(y-1)^2
sqrt(x-2/2)=sqrt((y-1)^2)
sqrt(x-2/2)=|y-1|
|y-1|=sqrt(x-2/2)
We have that the absolute value of y-1 is equal to sqrt(x-22). This means that we have two solutions, one positive and one negative. |y-1|=sqrt(x-2/2) ⇒ lc y-1 ≥ 0:y-1 = sqrt(x-2/2) & (I) y-1 < 0:y-1 = - (sqrt(x-2/2)) & (II) Now we can fully isolate y.
y-1=sqrt(x-22) y-1=-sqrt(x-22)
y=sqrt(x-22)+1 y=-sqrt(x-22)+1