Question

Solve the following equation and check your results(s):
$8x + 4 = 3\left( {x - 1} \right) + 7$

Answer 1

Hint: Separate the terms containing $x$ on one side and constants on the other. Solve the equation, find the value of $x$ and put it again in the initial equation to verify the result.

Complete Step-by-Step solution:
The given equation is:
$ \Rightarrow 8x + 4 = 3\left( {x - 1} \right) + 7 .....(i)$
Separating the terms containing $x$ on one side and constants on the other and simplifying this further, we’ll get:
$
   \Rightarrow 8x + 4 = 3x - 3 + 7 \\
   \Rightarrow 8x - 3x = 4 - 4 \\
   \Rightarrow 5x = 0 \\
   \Rightarrow x = 0 \\
$
The value of $x$ in the above equation is 0.
For verifying result put $x = 0$in equation $(i)$, we’ll get:
$
   \Rightarrow 8 \times 0 + 4 = 3 \times 0 - 3 + 7 \\
   \Rightarrow 0 + 4 = 0 - 3 + 7 \\
$
$
   \Rightarrow 4 = 4 \\
   \Rightarrow {\text{LHS = RHS}} \\
$
Therefore, $x = 0$ is the solution of the above equation.

Note: Linear equations in one variable can be solved straight away by separating terms. If the equation is in two variables then we need another equation to solve. In fact we need as many equations to find a unique solution of a system of equations as the number of variables in the system.