Question

How do you solve $\dfrac{{x - 3}}{4} + \dfrac{x}{2} = 3$ ?

Answer 1

Hint: First, we shall analyze the given data so that we can able to solve the problem. Here we are given an algebraic equation. Here, we need to solve the given equation $\dfrac{{x - 3}}{4} + \dfrac{x}{2} = 3$
To solve the given equation, we shall cross-multiply on both sides and we need to take the constant to one side of the equation.

Complete step-by-step answer:
Here, we need to solve the given equation $\dfrac{{x - 3}}{4} + \dfrac{x}{2} = 3$
Now, we shall cross-multiply on both sides.
$\dfrac{{2\left( {x - 3} \right) + 4x}}{{4 \times 2}} = 3$
$ \Rightarrow \dfrac{{2x - 6 + 4x}}{8} = 3$
$ \Rightarrow \dfrac{{6x - 6}}{8} = 3$
$ \Rightarrow 6x - 6 = 3 \times 8$
$ \Rightarrow 6x - 6 = 24$
$ \Rightarrow 6x = 24 + 6$
$ \Rightarrow 6x = 30$
$ \Rightarrow x = \dfrac{{30}}{6}$
$ \Rightarrow x = 5$
Thus, we have solved the given equation.

Additional information:
The simplification of an expression is the process of changing the expression effectively without changing the meaning of an expression.
Moreover, various steps are involved to simply an expression and some of the steps are listed below:
When the given expression contains like terms, we need to combine them.
Example: $3x + 2x + 4 = 5x + 4$
We need to split the given expression into factors (i.e) the process of finding the factors for the given expression.
Example: ${x^2} + 4x + 3 = (x + 3)(x + 1)$
We need to expand an algebraic expression (i.e) we have to remove the respective brackets of an expression.
Example: $3(a + b) = 3a + 3b$.
We need to cancel out the common terms in an expression.
Example: $\dfrac{{{x^2} + 4x + 3}}{{x + 1}} = \dfrac{{(x + 3)(x + 1)}}{{x + 1}}$
$ = x + 3$
Also, we need to apply the BODMAS rule (i.e.) we need to calculate the brackets first and then orders, then division or multiplication, and finally we need to add or subtract.

Note: Also, it is to be noted that an equation can be an algebraic equation, a trigonometric equation, a logarithmic equation or, a differential equation. Here we are given an algebraic equation. Further, to solve these types of equations, we should be aware of algebraic identities, trigonometric identities. Also, we need to check whether we are given an algebraic equation or an algebraic expression. An expression is a combination of variables and constants that are expressed together whereas an algebraic equation is a combination of variables and constants that are equated to another combination.