Unit 3: Equations

Solutions to Equations

100

Solve the equation.

2x(x + 3) - 5x² + 9x = -3x² + 15x

Infinite Solutions

200

Solve the equation.

-5(-2 - 8m) = 10 + 5m

m = 0

300

Solve the equation.

-(3 - 6b) = -4b -7 + 10b + 2

No solution.

400

Solve the equation.

−11 + 10(p + 10) = 4 − 5(2p + 11)

p = -7

500

Solve the equation.

6 - 2(4v+6) + 2 = 3 - 10v - 7 + 2v

Infinite Solutions

Changing the Subject

100

Make y the subject of the equation.

t + 7y = c + r

y = (c+r-t)/7

200

Make x the subject of the equation.

x³ - 4 = 5y

x=root(3)(5y+4)

300

Make x the subject of the equation.

m = (a)/(x+2

x = a/m-2

400

Make m the subject of the equation.

a - (2sqrtm)/3=b

m = ((-3(b-a))/2)^2

m = ((3(b-a))/-2)^2 

m = ((3(a-b))/2)^2

500

Make d the subject of the equation.

a^2d^2-b^2=b^2c^2

 d=+-sqrt((b^2c^2+b^2)/(a^2) 

OR FULLY SIMPLIFIED

+-(bsqrt(c^2+1))/a

Radical Equations

100

Solve.

sqrt(3x+1)=4

x = 5

200

Solve.

sqrt(x-3)=x-5

x = 7

4 is an extraneous solution.

300

Solve.

2sqrt(2x+5)-x=4 

x =  +-2 

400

Solve.

sqrt(x+10)-2=sqrt(x+2)

x = -1

500

Solve.

sqrt(x+16)-sqrt(x)=2

x = 9

Product Rule of Roots

100

Evaluate and simplify your final answer.

sqrt(8)*sqrt(5)

2sqrt(10)

200

Evaluate and simplify your final answer.

2sqrt(3)*4sqrt(8) 

16sqrt(6)

300

Evaluate and simplify your final answer.

sqrt(18)*sqrt(32) 

24

400

Evaluate and simplify your final answer.

(2+sqrt(3))^2 

7+4sqrt(3)

500

Evaluate and simplify your final answer.

(sqrt10 +4)*(3-sqrt10) 

-sqrt(10)+2