Solve the following equation - Junior Cycle Mathematics - Question 11 - 2013
Question 11
Solve the following equation. Give your answer in the form \( \frac{m}{n} \) where \( m, n \in \mathbb{N} \).
\[ \frac{3x + 5}{2} + \frac{x - 4}{3} = 16 \]
Worked Solution & Example Answer:Solve the following equation - Junior Cycle Mathematics - Question 11 - 2013
Step 1
Combine the Fractions with a Common Denominator
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To solve the equation, first, we find a common denominator for the fractions. The denominators are 2 and 3, so the common denominator is 6. Rewriting the fractions gives us:
[ \frac{3(3x + 5)}{6} + \frac{2(x - 4)}{6} = 16 ]
This simplifies to:
[ \frac{9x + 15 + 2x - 8}{6} = 16 ]
Step 2
Clear the Denominator
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Next, we multiply both sides by 6 to eliminate the denominator:
[ 9x + 15 + 2x - 8 = 96 ]
This simplifies to:
[ 11x + 7 = 96 ]
Step 3
Isolate the Variable
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Now we isolate ( x ) by subtracting 7 from both sides:
[ 11x = 96 - 7 ]
[ 11x = 89 ]
Step 4
Solve for x
98%
120 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Finally, we divide both sides by 11:
[ x = \frac{89}{11} ]
Thus, the answer is ( \frac{89}{11} ), where ( m = 89 ) and ( n = 11 ).
Join the Junior Cycle students using SimpleStudy...
