Question

If $\dfrac{{x + 1}}{2} + \dfrac{{4x - 1}}{4} = 5.5$, then find the value of $x$
A ) 2.5
B ) 3.0
C ) 3.5
D ) 4.0

Answer 1

Hint: Use the algebraic properties of solving equations in one variable. Segregate the terms containing the variable x on the left-hand side of the equation and the constant terms on the right-hand side of the equation.

Complete step by step solution:
We have been given that $\dfrac{{x + 1}}{2} + \dfrac{{4x - 1}}{4} = 5.5$
Taking LCM on the left-hand side of the given equation we get,
$\dfrac{{2\left( {x + 1} \right) + \left( {4x - 1} \right)}}{4} = 5.5$
Simplifying the numerator of the fraction on the left-hand side of the given equation by adding up similar terms, we get
$\dfrac{{6x + 1}}{4} = 5.5$
Taking the denominator on the left-hand side of the equation to the right-hand side of the equation, we get
$6x + 1 = \left( {5.5} \right) \times 4$
Further simplifying the right-hand side of the equation, we get
$6x + 1 = 22$
Segregating the term containing the variable and the constant terms on either side of the equation, we get
$\begin{array}{l}
6x = 22 - 1\\
 \Rightarrow 6x = 21
\end{array}$
Further simplifying the above equation, we get
$x = \dfrac{{21}}{6} = 3.5$

Thus, the third option is the correct option.

Note: Solving equations means having variable terms on one side and number on the other side. Linear equations in one variable are equations where the variable has an exponent of 1, which is typically not shown. To solve linear equations, there is one main goal: isolate the variable. Anytime you are solving linear equations, you can always check your answer by substituting it back into the equation. If you get a true statement, then the answer is correct. This is not 100% necessary for every problem, but it is a good habit.