Question

How do you solve \[37 = - 3 + 5\left( {x + 6} \right)\]?

Answer 1

Hint: The equation given in the question is a linear equation in one variable. Since it contains only one variable, the single equation is sufficient to obtain the solution. For this, we need to apply the basic algebraic manipulations on the given equation to separate the variable \[x\] and hence obtain its value.

Complete step-by-step solution:
We need to solve the equation \[37 = - 3 + 5\left( {x + 6} \right)\].
Since in the given equation, the highest power of the variable \[x\] is equal to one, the degree of the given equation is equal to one and hence the given equation is a linear equation.
Now adding \[3\] on both sides of the given equation, we get
\[37 + 3 = 5\left( {x + 6} \right)\]
\[ \Rightarrow 40 = 5\left( {x + 6} \right)\]
Now, we will divide both the sides by \[5\] to get
\[8 = x + 6\]
On subtracting \[6\] from both sides, we get
\[8 - 6 = x + 6 - 6\]
\[ \Rightarrow 2 = x\]
Or
\[x = 2\]

Hence, the given equation is solved and the solution of the given equation is \[x = 2\].

Additional information:
The given equation is a linear equation. A linear equation is an equation with the highest degree of variable as 2 and also has only 1 solution. When the highest degree of an equation is 2, then the equation is termed as a quadratic equation. Similarly, when the highest degree of an equation is 3, then the equation is termed as a cubic equation. So, we can differentiate an equation by observing the highest degree of the equation.

Note:
Here we can also solve the question using an alternate method.
To solve the equation \[37 = - 3 + 5\left( {x + 6} \right)\] we will first add 3 on both sides. Therefore, we get
\[ \Rightarrow 40 = 5\left( {x + 6} \right)\]
Now using the distributive property of multiplication, we get
\[ \Rightarrow 40 = 5x + 5 \times 6\]
Multiplying the terms, we get
\[ \Rightarrow 40 = 5x + 30\]
Subtracting 30 from both the sides, we get
\[\begin{array}{l} \Rightarrow 40 - 30 = 5x\\ \Rightarrow 10 = 5x\end{array}\]
Dividing both sides by 5, we get
\[ \Rightarrow x = 2\]