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.

Pearson Algebra 2 Common Core, 2011

PA

Pearson Algebra 2 Common Core, 2011 View details

End-of-Course Assessment

Finish the assignment

Exercise 19 Page 966

Factor the denominators, and multiply both sides of the equation by the least common denominator.

D

Practice makes perfect

We want to solve the given rational equation. 3/2x+10+5/4=7/x+5 We will start by factoring the denominators to find a least common denominator (LCD). Note that the second and the third denominator are already factored. Let's factor the first one.

2x+10

Factor out 2

2(x+5)

We can now rewrite the given expression. 3/2x+10+5/4=7/x+5 ⇕ 3/2 (x+5)+5/4=7/(x+5) The LCD is 4 (x+5) because it is the least common multiple of the denominators. We will solve the equation by multiplying each side by the LCD to clear denominators.

3/2(x+5)+5/4=7/x+5

LHS * 4 (x+5)=RHS* 4 (x+5)

(3/2(x+5)+5/4)* 4 (x+5)=7/x+5* 4 (x+5)

▼

Multiply

Distribute 4(x+5)

3/2(x+5)* 4(x+5)+5/4 * 4(x+5)=7/x+5 * 4(x+5)

CancelCommonFac

Cancel out common factors

3/2(x+5)* 4(x+5)+5/4 * 4(x+5)=7/x+5 * 4(x+5)

Simplify quotient

3/2* 4+5(x+5)=7* 4

MoveRightFacToNum

a/c* b = a* b/c

3* 4/2+5(x+5) =7 * 4

Multiply

12/2+5(x+5) =28

Calculate quotient

6+5(x+5)=28

Distribute 5

6+5x+25=28

Add terms

31+5x=28

LHS-31=RHS-31

5x=- 3

.LHS /5.=.RHS /5.

x=- 3/5

MoveNegNumToFrac

Put minus sign in front of fraction

x = - 3/5

This corresponds to option D.

Subchapter links

Exercises p.964-971