Question

How do you solve \[4x + 4 = 6x - 14\] ?

Answer 1

Hint: The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. The given equation is a linear equation as there is a constant variable involved and to solve the given inequality, combine all the like terms and then simplify the terms to get the value of \[x\].

Complete step by step solution:
Let us write the given equation
\[\Rightarrow 4x + 4 = 6x - 14\]
To get the combined terms, subtract 4 on both the sides of the given equation
\[\Rightarrow 4x + 4 - 4 = 6x - 14 - 4\]
As we can see that -4 and +4 implies zero.
\[\Rightarrow 4x = 6x - 14 - 4\]
Simplifying the numbers in the equation, we get
\[\Rightarrow 4x = 6x - 18\]
As the equation consists of like terms, so let us combine all the like terms and simplify it
\[\Rightarrow 4x - 6x = - 18\]
\[ \Rightarrow \] \[ - 2x = - 18\]
Now divide both sides of the equation by the same term i.e., -2 we get
\[\Rightarrow \dfrac{{ - 2x}}{{ - 2}} = \dfrac{{ - 18}}{{ - 2}}\]
We can see that the numerator term and denominator term both are the same which implies one with the remaining \[x\] term, as we need to get the value of \[x\]. Hence, we get
\[\Rightarrow x = \dfrac{{ - 18}}{{ - 2}}\]
Therefore, we get the value of \[x\] as
\[\Rightarrow x = 9\]
Hence, the value of \[x\] in the given equation is \[x = 9\].

Additional information: Equations that have more than one unknown can have an infinite number of solutions, finding the values of letters within two or more equations are called simultaneous equations because the equations are solved at the same time. There are three methods to solve the system of linear equations in two variables: Substitution method, Elimination method and Cross-multiplication method.

Note: The key point to solve this type of equation is to combine all the like terms i.e., finding out the common term and evaluate for the variable asked. As we know that Simultaneous equations are two equations, each with the same two unknowns and are simultaneous because they are solved together.