Linear Equations and Inequalities

Solving Equations

100

3(x+1)=12

x=3

200

4(x+6) = 10x 

x=4

300

-2(x-2)-6 = 3(x+5)

x=-5

400

(1/2)*(x+2) = (1/4)*(x-2)

x = -6

500

(x/3)-(x/4)=5

x=60

Solving Inequalities

100

2x + 5 < 3

x < -1

200

-2x + 27 < 5x + 6

x > 3

300

2(x+4) > 5x + 7

x < 1

400

(1/2)(x+3) < -2x +5

x < (7/5)

500

(x/5) - (x/3) > (8/15)

x < -4

Solving Formulas

100

The formula for work is

W = dF

Derive an equation for F in terms of W and d

F = W/d

200

The formula to convert between Celsius and Fahrenheit is

F = (9/5)(C + 32)

Derive an equation for C in terms of F

C = (5/9)F - 32

300

The volume of a pyramid is given by the equation 

V = (1/3)*Bh

Derive an equation for h in terms of B and V

h = 3V/B

400

The equation for distance is 

d = v(t₂-t₁)

Derive an equation for t₁ in terms of d, v, and t₂

t₂ = t₁ - d/v

500

The equation for light reflecting in a mirror is

(1/d₁) + (1/d₂) = (1/f)

Derive an equation for d₂ in terms of d₁ and f

d₂ = (-d₁f)/(f-d₁)

Solving for Variables

100

A = B + 2C

Derive an equation for B in terms of C and A

B = A - 2C

200

(2a+2c)/4 = b

Derive an equation for c in terms of a and b

c = 2b - a

300

(1/2)(a+b) = (1/4)(c+d)

Derive an equation for b in terms of a, c, and d

b = (c+d-2a)/2

400

(fm/2) + c = 2d

Derive an equation for m in terms of c, d, and f

m = (4d-2c)/f

500

(a/c) + (1/2) = (2d/e)

Derive an equation for c in terms of a, d, and e

c = a/((2d/e) - (1/2))

Solve for y in terms of x

100

2x + 4y = 8

y = 2 - (1/2)x

200

4x - 3y = 12

y = (4/3)x - 4

300

3x - 4y = 16

y = (3/4)x - 4

400

-5x - 2y = 8

y = (-5/2)x - 4

500

(3/4)x - (1/2)y = 3

y = (3/2)x - 6