Exercise 181 Page 117

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

SubEqn

LHS-4=RHS-4

-2(x+y)=5

DivEqn

.LHS /(-2).=.RHS /(-2).

x+y=5/-2

MoveNegDenomToFrac

Put minus sign in front of fraction

x+y=-5/2

SubEqn

LHS-x=RHS-x

y=- x-5/2

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

SubEqn

LHS-2=RHS-2

x-2=2(y-1)^2

DivEqn

.LHS /2.=.RHS /2.

x-2/2=(y-1)^2

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(x-2/2)=sqrt((y-1)^2)

SqrtToAbs

sqrt(a^2)=|a|

sqrt(x-2/2)=|y-1|

RearrangeEqn

Rearrange equation

|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)

AddEqn

LHS+1=RHS+1

y=sqrt(x-22)+1 y=-sqrt(x-22)+1

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Exercise 181 Page 117

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