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!