SAT Mc Graw Hill 2011

CHAPTER 8 / ESSENTIAL ALGEBRA I SKILLS 303

5.

Multiply by 3: 2 x^2 = 3 x^2

Subtract 2x^2 :0 =x^2

Take square root: 0 =x

6.

Cross-multiply: 2 x+ 4 = 3 x− 15

Subtract 2x: 4 =x− 15

Add 15: 19 =x

7. Operation: Multiply both sides by 4
   Solution: 10x+ 12 = 28


8. Operation: Divide both sides by 3
   Solution: 6y+ 4 =7/3

xx+

=

2 −

3

5

2

2

3

2
x =x 2
Concept Review 1

1. The laws of equality say that whatever you do to
   one side of an equation you must do to the other
   side, to maintain the balance.


2. Yes. Dividing by 0 and taking the square root of a
   negative number are “undefined” operations in the
   real numbers. Be careful, then, when dividing both
   sides of an equation by an unknown, to check that
   the unknown could not possibly be 0.


3. 9 x− 12 + 5 x= 3 x
   Commutative law: 14 x− 12 = 3 x
   Add 12, subtract 3x: 11 x= 12
   Divide by 11: x=12/11


4. (x−4)^2 = 5

Take square root:

Add 4: x=± 45

x−=± 45

Answer Key 1: Solving Equations

SAT Practice 1

1.C 5 d+ 12 = 24
Subtract 24: 5 d− 12 = 0
2.A Translate into an equation: x− 7 = 5 x
Subtract x: − 7 = 4 x
Divide by 4: −7/4 =x
You can also “test” the choices and see which one
works, but that’s probably more time-consuming.

3. 5 It’s easiest to solve the equation for y,then
   add 5

Multiply by 5: 2 y^2 = 5 y^2

Subtract 2y^2 :0 = 3 y^2

Divide by 3: 0 =y^2

Take the square root: 0 =y

Add 5: 5 =y+ 5

4.E 2 x^2 − 5 x= 9

Multiply by 6: 12 x^2 − 30 x= 54

5.D Plugging in and checking is perhaps easiest

here, but you could do the algebra too:

(p+2)^2 =(p−5)^2

FOIL: p^2 + 4 p+ 4 =p^2 − 10 p+ 25

Subtract p^2 :4p+ 4 =− 10 p+ 25

Subtract 4: 4 p=− 10 p+ 21

Add 10p: 14 p= 21

Divide by 14: p=1.5

2

5

2

y =y 2

6.A

Multiply by 5x: 25 + 7 x= 5 x

Subtract 7x: 25 =− 2 x

Divide by −2: −25/2 =x

7.C Guess and check here. If x=−36 and y=−1,

or x=1 and y=36, then x−y=−35.

8.E Just plug in the points (−1, 7) and (1, 3) to the

equations, and confirm that the points “satisfy”

all three equations.

9.C

Subtract 20:

Multiply by −1:

Square both sides: x= 81

10.D = 2

Multiply by m−nx: 3 x=2(m−nx)

Distribute on right: 3 x= 2 m− 2 nx

Add 2nx: 3 x+ 2 nx= 2 m

Factor left side: x(3 + 2 n) = 2 m

Divide by (3 + 2 n): x m

n

=

+

2

32

3 x

mnx−

x= 9

−=−x 9

20 −=x 11

57

5

1

x

+=