Solving Linear Equations

Solving Equations

100

Solve the equation: 3x - 11 = x + 13 

x = 12 

200

Solve the equation: -4x + 12 = 2x - 18 

x = 5

300

Sherley solved the following equation. Tell which step she made a mistake in:

Equation: -12x + 13 = -11x + 12

Step 1: -1x + 13 = 12

Step 2: -1x = 25

Step 3: x = -25 

Step 2

400

Solve the equation:

110x - 350 = 12x - 154 

x = 2

Distributive Property

100

Simplify the expression: -3(-2x - 1) 

6x + 3 

200

Solve the equation:

2(3x - 1) = 7x - 12 

x = 10

300

Solve the equation"

-9(x - 1) = 3x + 12 

x = -3/12 or -1/4 

400

John solved the following equation. Tell which step he made a mistake in:

Equation: -3(x - 12) = 4(x + 1)

Step 1: -3x - 36 = 4x + 4

Step 2: -7x - 36 = 4

Step 3: -7x = 40 

Step 4: x = -40/7 

Step 1 

Fractions

100

Solve the equation: 

1/2 x-1=3x+2

x = -6/5 

200

Solve the equation: 

1/3x-3=1/2x+2

x = -30 

300

Solve the equation: 

1/3(3x-9) = 1/2 x+1

x= 8

400

Jayson solved the following equation. Explain which step he did incorrectly: 

Equation: 

1/6(6x-12) = 12x-6

Step 1: x - 2 = 2x - 1

Step 2: -x - 2 = -1

Step 3: -x = 1 

Step 4: x = -1 

Step 1 

How many solutions?

100

How many solutions does the equation have:

3x - 12 = 3x + 11

None 

200

Which equation has infinitely many solutions:

a. 3(x - 1 ) = 3x - 1

b. 3(x - 1) = 3x + 3

c. 3(x - 1) = 4x - 3 + x

d. 3(x-1) = 4x - 3 - x

d. 3(x-1) = 4x - 3 - x

300

Consider the following part of an equation:

6(x-4)+12 = _____________. 

What could be put in the blank so that the equation has infinitely many solutions? 

a. 6x - 12

b. 6x + 12

c. 6x - 24

d. 6x + 24 

a. 6x - 12 

400

Give an example of an equation that has no solution. 

Answers may vary. Examples:

-4x + 1 = -4x - 12

3x - 2 = 3x + 2

2x +11 = 2x + 1