Solve the equation and check your answer
(q+9)/5 + (q-2)/2 = 11/5
(q+9)/5 + (q-2)/2 = 11/5
We identify the common denominator as 10. By multiplying both sides of the equation by the common denominator, we end up with integer coefficients, which are easier to work with.
2(q+9) + 5(q-2) = 22
Next we use distributivity to expand the expressions on the left:
2q + 18 + 5q -10 = 22
Then we group like terms in q on the left, and constants on the right:
2q + 5q = 22 -18 + 10
Simplify and reduce:
7q = 14
Divide by the coefficient of the unknown (7) on both sides:
q = 2
The last step is to substitute the value of q in the original equation and verify that the solution is correct.