If a rectangle has area 48cm2 and sides length 6cm and (3x+2)cm, what is the value of x?

First we need to look at the important information and draw a diagram (on whiteboard).

Now, we know that the area of the rectangle is 48cm2 and that the area of any rectangle is:

length side a x length side b

In this question, side a has length 6cm and side b has length (3x+2)cm.

Therefore we can form the equation:

6 x (3x+2) = area of rectangle = 48

Now we have a linear equation that we need to solve: 6 x (3x+2) = 48 

Firstly, we can simplify by expanding the brackets:

18x + 12 = 48

Then minus the 12 from both sides

18x = 36

And divide by 18

x = 2

Now we have an answer x=2, but we must always check that this is correct by testing it in the original equation:

6 x (3x+2) = 48

6 x ((3x2)+2) = 48

6 x (6+2) = 48

6 x 8 = 48

48 = 48

Therefore, we have verified that x=2 is the correct answer!