body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Core Connections Algebra 2, 2013

CC

Core Connections Algebra 2, 2013 View details

2. Section 4.2

Finish the assignment

Continue to next subchapter

Exercise 87 Page 194

Practice makes perfect

a To solve the equation for y, we have to simplify the left-hand side and then perform inverse operations until y is isolated.

x-3(y+2)=6

Distribute -3

x-3y-6=6

LHS+3y=RHS+3y

x-6=6+3y

LHS-6=RHS-6

x-12=3y

Rearrange equation

3y=x-12

.LHS /3.=.RHS /3.

y=x-12/3

Write as a difference of fractions

y=x/3-12/3

Calculate quotient

y=x/3-4

a/b=1/b* a

y=1/3x-4

b Like in Part A, we have to perform inverse operations until y is by itself.

6x-1/y-3=2

LHS+3=RHS+3

6x-1/y=5

LHS * y=RHS* y

6x-1=5y

Rearrange equation

5y=6x-1

.LHS /5.=.RHS /5.

y=6x-1/5

Write as a difference of fractions

y=6x/5-1/5

MovePartNumRight

a* b/c=a/c* b

y=6/5x-1/5

Since the equation started out with y in the denominator, y cannot equal 0.

c To isolate y, we need to remove the radical sign. If we raise both sides to the power of 2, the radical and the power will cancel each other.

sqrt(y-4)=x+1

LHS^2=RHS^2

y-4=(x+1)^2

LHS+4=RHS+4

y=(x+1)^2+4

We have now isolated y and it's not necessary to expand the parentheses, because this form is possible to enter in the calculator. Note that in the original equation y cannot be less than -4.

d Like in Part C, we will raise both sides to the power of 2 to eliminate the radical sign.

sqrt(y+4)=x+2

LHS^2=RHS^2

y+4=(x+2)^2

ExpandPosPerfectSquare

(a+b)^2=a^2+2ab+b^2

y+4=x^2+4x+4

LHS-4=RHS-4

y=x^2+4x

Note that In the original equation y must be greater or equal to -4. Otherwise, we will end up with a negative argument under the square root which is undefined.

Subchapter links

4.2.1 Solving Inequalities with One or Two Variables p.188-190

4.2.2 Using Systems to Solve a Problem p.193-194

4.2.3 Application of Systems of Linear Inequalities p.197-198

4.2.4 Using Graphs to Find Solutions p.200-201