2j 18 3 1.Solve the proportion using the cross-product property: 5 j + 6 j = Apply cross product...

2j18

3

1. Solve the proportion using the cross-product property:

5 j + 6 j

= Apply cross product property

3 (j + 6) = • j 5

3j + 18 = 5j

Distribute

22

9 = j

– 3j– 3j

Subtract

= Divide

Algebra I Concept Test # 18 – Rational Ex. & Proportions Practice Test

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3

2. Check solution for # 1

5 j + 6 j

=

5

9 + 6=

9

3Substitute

; 9 = j

Simplify

Equation and solution

5

15= 3

3 = 3

Check


8

4 • 7


7 2m 8

m= Apply cross product property

2m• m = • 7 Simplify

2m2 = 56 Divide 22

m2 = 28 Square Root

m = 2 7

+

+


m = Perfect square factor+

Simplify

2


a – 28 a + 4

= Apply cross product property

8 • 2 = (a + 4)(a – 2)

16 = a2 + 4a – 2a – 8

Multiply

Combine

16 = a2 + 2a – 8

– 16– 16Subtract

0 = a2 + 2a – 24 Factor

0 = (a + 6)(a – 4) Zero product property

0 = a + 6 0 = a – 4 Solve

− 6 = a

4 = a


5. Simplify: 32x2

* Factor each term into it’s prime factorization

32x2 2 • 2 • 2 • 2 • 2 • x • x

24x 2 • 2 • 2 • 3 • x

* Reduce the common factors

24x

2 • 2 • 2 • 2 • 2 • x • x

2 • 2 • 2 • 3 • x

2 • 2 • x

3

4x

3


r(r – 2)

4

6. Simplify:

3r3 – 6r2

12r

* Factor the greatest common factor from the binomial in the numerator

3r2(r – 2)

12r

* A monomial may only reduce with another monomial

r

4


* Simplify implies that all operations are performed

= r2 – 2r

4Multiply

7. Simplify:

y – 3

y2 – 10y + 21 (y – 7)2 • Expand

y – 3

y2 – 10y + 21 (y – 7)(y – 7) • Factor denominator

y – 3

(y – 7)(y – 3) (y – 7)(y – 7) • Reduce

* Any binomial term in the numerator may reduce with any binomial term in the denominator

(y – 7)



w – 9

71

21w

8. Simplify:

21w 2w + 9 w – 9

+

2w + 9 +

3w

21w

Combine like terms

Reduce

* Notice, the fractions have like denominators. Add the numerators and place over common denominator

21w

1

7


2x + 4 2x + 4

9. Simplify:

5x2 – 5x − 2x2 + 7x – 8+

* Notice, the fractions have like denominators. Add the numerators and place over common denominator

3x2 + 2x – 8

2x + 4

2x + 4

(3x – 4)(x + 2)

Factor the numerator

2(x + 2)

(3x – 4)(x + 2)

Factor the denominator

Reduce

2

3x – 4

5h2 + 2h – 16 5h2 + 2h – 16

10. Simplify:

7h – 2 2h + 6–

* Notice, the fractions have like denominators. Subtract the numerators and place over common denominator

(2h + 6) 7h – 2 – Combine like terms5h2 + 2h – 16

5h – 8

5h2 + 2h – 16 Factor the denominator

5h – 8

(5h – 8)(h + 2)

1

h + 2


Reduce


11. Simplify:

− 1

x2

x2 x 5 1 + 5x –

* To add fractions we need common denominators

* The common denominator is x2

x2 x 5 1 + 5x

– • x

• x

x2 x2

5x 1 + 5x –

* The fractions have like denominators, subtract the numerators

x2

5x – 1 – 5x

• 2x


12. Solve:

21

x2

x3

=+

* To solve a fractional equation multiply each term by the LCD

* The LCD is 2x

21

x2

x3

=+ • 2x• 2x

Reduce

Multiply

22x

x4x

x6x

=+

x + 4 = 6

x = 2

– 4– 4Subtract


13. Solve:

x + 14

1=+1

x – 2

* To solve a fractional equation multiply each term by the LCD

* The LCD is (x + 1)(x – 2)

x + 14

1=+1

(x – 2)

(x + 1)(x – 2) (x + 1)(x – 2)

(x + 1)(x – 2)

Reduce4(x – 2) + 1(x + 1) = 1(x + 1)(x – 2)

Multiply4x – 8 + x + 1 = x2 – 2x + x – 2


13cont. Solve:

Combine like terms

5x – 7 = x2 – x – 2– 5x– 5x

Subtract

− 7 = x2 – 6x – 2+ 7+ 7

Add

0 = x2 – 6x + 5 Factor

0 = (x – 5)(x – 1) Zero product property

0 = x – 5 0 = x – 1 Solve

5 = x

1 = x

4x – 8 + x + 1 = x2 – 2x + x – 2

x + 14

1=+1

x – 2

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