Solve the following eqation for x: 6(4x+5)+3=3(x+8)+3. round to the nearest hundredth

24x + 33 = 3x + 27

21x + 33 = 27

21x = -6

X = -.29

Subtract 3 from both sides

6(4x + 5) + 3 - 3 = 3( x + 8) + 3 - 3

Simplify

6( 4x + 5) = 3(x + 8)

6(4x + 5)

a(b + c) = ab + ac

a = 6, b = 4x, c = 5

= 6 x 4x + 6 x 5

6 x 4x + 6 x 5

Multiply the numbers: 6 x 4 = 24

= 24x + 6 x 5

Multiply the numbers: 6 x 5 = 30

= 24x + 30

3(x + 8)

a(b + c) = ab + ac

a = 3, b = x, c = 8

= 3x + 3 x 8

Multiply the numbers: 3 x 8 = 24

= 3x + 24

24x + 30 = 3x + 24

Subtract 30 from both sides

24x + 30 - 30 = 3x + 24 -30

Simplify

24x = 3x - 6

Subtract 3x from both sides

24x - 3x = 3x - 6 - 3x

Simplify

21x = -6

Divide both sides by 21

21x/21 = -6/21

Note: Simplify -6/21 to get the value for x.

Answer in fraction: x = -2/7

Answer in decimal rounded to the nearest hundredth: x = -0.29

I know this seems complicated; that's why I did it step by step.

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)