2. Solve this inequality. Show your work. 5.6+2.2.x > 65.6-1.8x

x>15

Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality:

          (56/10)+(22/10)*x-((656/10)-(18/10)*x)>0  

Simplify   9/5

  56  22      656  9

 (——+(——•x))-(———-(—•x))  > 0  

  10  10      10   5

Simplify 328/5

  56  22      328 9x

 (——+(——•x))-(———-——)  > 0  

  10  10       5  5  

Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

328 - (9x)     328 - 9x

——————————  =  ————————

    5             5    

  56/10+22/10.x/5)) >0      (328 - 9x)

Simplify  11/5

  56/10+11/5.x/5))->0 (328-9x  

Simplify 28/5

  28    11x     (328 - 9x)

 (—— +  ———) -  ——————————  > 0  

  5      5          5      

Adding fractions which have a common denominator

     Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

28 + 11x     11x + 28

————————  =  ————————

   5            5    

:

 (11x + 28)    (328 - 9x)

 —————————— -  ——————————  > 0  

     5             5      

Adding fractions which have a common denominator

       Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(11x+28) - ((328-9x))     20x - 300

—————————————————————  =  —————————

          5                   5    

   Pull out like factors :

  20x - 300  =   20 • (x - 15)  

 20 • (x - 15)

 —————————————  > 0  

     Multiply both sides by  5  

   Divide both sides by  20  

Solve Basic Inequality :

  Add  15  to both sides

            x > 15

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.