Hi. Please help me with the following question.

Question

1) Solve the following equations using inverse operations.

i) 3x-7=7+x

ii) 3[(6x-2)/4 (Separate)+ 1 ] = 33

2) A cylindrical (cylinder) water tank of diameter 2.2m and height of 3m is full of water. The water flows out of the base into a rectangular prism 7m long and 3m wide.

a) Find the volume of the water in the cylindrical water tank in:
i) cubic metres
ii) litres 

b) Let the height of the rectangular prism be hm. Find the volume of the rectangular prism (box) in terms of h. Do this by writing the formula for the volume of a rectangular prism and substituting in the two known values and h.

c) What would the minimum height (h, to the nearest cm) of the rectangular prism have to be if it is to hold all the water. 

Thanks so much!!

Answer 1

i) 3x-7=7+x  To solve by using inverse operations just means that you should combine like terms.

First, add the opposite of x to each side (or you may be permitted to mentally subtract x from each side, equivalently).

Then add 7 to both sides.  Finally, isolate the variable by dividing both sides by the coefficient of the variable (division by the coefficient gives new coefficient one). Don't forget to check your answer.