Solving Equations Review

Number of Solutions

100

True or False: A linear equation has ONE solution when the variable equals zero.

True  (x=0)

200

How many solutions does this equation have?

2x - 8 = 2x - 2(4)

Infinitely Many Solutions

300

How many solutions does this equation have?

2x + 5 = 2x + 8

No Solutions  

(5 = 8)  False!

400

How many solutions does this equation have?

y + 13 + 7y - 7 = 2 (4y + 3)

Infinitely Many Solutions

500

How many solutions does this equation have?

25 - 2z - 10z = -3 (4z + 8) - 1

No solutions

Literal Equations

100

Solve for x:  ax - b = c

x = (b + c)/a

200

Solve for b:  P = a + b + c

b = P - a - c

300

Solve for P:  A = P (1 + r)

P = A / (1+r)

400

Solve for c:  15 = -5 (2c + d)

c = (-3 - d) / 2

500

Solve for x:  2/3 (x - 18y) = 6y

x = 27y

Multistep Equations

100

Solve for m:  -2 = -7m + 6m

m = 2

200

Solve for a:  -3 (2a - 3) + 1 = -20

a = 5

300

Solve for x:  -20 = -2 (5 + 6x) + 14

x = 2

400

Solve for x:  -3 (3x + 15) - (x + 10) = 35

x = -9

500

Solve for x:  -4 (x - 3) = -6 (x - 1)

x = -3

Variables on Both Sides Equations

100

Solve for m: 4m + 2 = -3m + 16

m = 2

200

Solve for x:  2 + x = 1 + 6 (7x + 7)

x = -1

300

Solve for w: 4w + 2 - w = 7 - 2w

w = 1

400

Solve for r: 4r + 39 = 5 ( 5 - 2r )

r = -1

500

Solve for n: -5 (8n - 4) - n = - 16 - 5n

n = 1

Translating Equations

100

The difference of a number and 25 is 100

x - 25 = 100

200

The quotient of a number and -2 is 12

x / -2 = 12

300

Two times the sum of a number and 5 is 20

2 (x + 5) = 20

400

One less than the product of a number and 3 is 5 more than the number itself

3n - 1 = 5 + n

500

Five times the sum of a number and 10 is a number squared increased by 4

5 (x + 10) = x² + 4