Question

How do you solve $5x - 4 = 2x - 7?$

Answer 1

Hint: To solve the given equation for the value of $x$, first of all simplify the equation with the help of algebraic operation in such a way that all variable should be on the left hand side whereas all constants should be on right hand side. After simplifying the equation in this way divide both sides with the coefficient of $x$ to get the final solution.

Complete step by step solution:
In order to solve the given equation $5x - 4 = 2x - 7$, we will first simplify the equation to send all variables at left hand side and constant at right hand side as follows
\[ \Rightarrow 5x - 4 = 2x - 7\]
Adding $4$ to both sides of the equation, in order to remove the constant from left hand side, we will get
\[
   \Rightarrow 5x - 4 + 4 = 2x - 7 + 4 \\
   \Rightarrow 5x = 2x - 3 \\
 \]
Now, subtracting $2x$ from both sides of the equation, in order to remove the variable from right hand side, we will get
\[
   \Rightarrow 5x - 2x = 2x - 3 - 2x \\
   \Rightarrow 3x = - 3 \\
 \]
So, we have simplified the equation in the considered way, that is variables on the left hand side and constants on the right hand side,
Now dividing both sides of the equation with the coefficient of the variable which is $3$ in this equation, we will get
\[
   \Rightarrow \dfrac{{3x}}{3} = \dfrac{{ - 3}}{3} \\
   \Rightarrow x = - 1 \\
 \]
Therefore \[x = - 1\] is the required solution for the given equation.

Note: When performing the algebraic operations to simplify the equation, always perform algebraic equation to both of the sides in order to maintain the balance of the equation. Otherwise the equation gets incorrect and hence the solution will be. We can solve this problem graphically too, by just plotting its graph and seeing where the graph cuts x-axis.