solve the linear equation |x+1|=2x+3

Question

1.solve the linear equation |x+1|=2x+3

 

2. solve the inequality and write the answer in interval notation x-2/4-x+1/2= great then equal to 1

 

3. a farmer sells kidney for 65 cents per pound and pinto beans for 85 cents per pound. how many pounds of kidney beans and pinto beans must the farmer use in order to make mixture of 120 pounds that he can sell for 73 cents per pound

Answer 1

1. |x+1|=2x+3

        Either, x+1=2x+3 or x+1=-(2x+3)

       1 -3=2x-x

-2=x

OR

x+1=-(2x+3)

x+1=-2x - 3

x + 2x = -1 -3

3x = -4

 x = -4/3

 

2.  Rewrite this inequality. You will end up with an untrue mathematical statement , 0≥1.

 

3. Assign variables for the amount in pounds of the beans:

let k represent the amount in pound of the kidney beans

and p represent the amount in pounds of the pinto beans. Then write the equations as described by the problem. You will have two unknowns and a system of equations. Solve using any method:

 

k + p = 120

0.65k  +  0.85p = 0.73(120)

 

k= 120 - p

0.65(120 - p) + 0.85p = 87.6    (Plug in equation 1 into eqn 2)

78 - 0.65p + 0.85p = 87.6

0.20p = 87.6  - 78

0.20p = 9.6

       p = 48

 

Solve for k,

k + 48 = 120

  k  = 72

The mixture that sales at 73 cents per pound will have 72 pounds of kidney beans and 48 pounds of pinto beans.