Find the value of the expression $$\frac{2x+1}{3} + \frac{3x-5}{2}$$ when $x = 7$ - Junior Cycle Mathematics - Question 12 - 2014

To express the equation as a single fraction, find a common denominator, which is 6:

$\frac{2(2x+1)}{6} + \frac{3(3x-5)}{6}$

This simplifies to:

$\frac{4x + 2 + 9x - 15}{6} = \frac{13x - 13}{6} = \frac{13(x-1)}{6}.$

To check the answer from part (b), substitute $x = 7$ into $\frac{13(x-1)}{6}$:

$\frac{13(7-1)}{6} = \frac{13(6)}{6} = \frac{78}{6} = 13.$

This matches the value found in part (a), confirming the answer.

Starting from part (b):

Rewriting the equation:

$\frac{13(x-1)}{6} = \frac{13}{2}$.

Cross-multiply:

$13(x-1) = 6 \cdot 13$.

This simplifies to:

$x-1 = 6 \\ x = 6 + 1 \\ x = 7.$