Question

Describe and correct the error in solving the equation

4x + 7 = x – 2

Short answer

The error is in first step where the sum of x and $-4x$ is written as $3x$ instead of $-3x$.

The correct solution of the equation will be $x=-3$

Step-by-step solution

Step-1 – Given

The given equation is $4x+7=x-2$.

Step-2 – To determine

We have to describe and correct the error..

Step-3 – Calculation

The provided solution of the equation is:

$\begin{array}{l}4x+7=x-2\\ 4x+7-4x=x-2-4x\\ 7=3x-2\\ 7+2=3x-2+2\\ 9=3x\\ 3=x\end{array}$

From, the given solution, we see that the error occurred in first step where the sum of x and $-4x$ is written as $3x$instead of $-3x$.

The solution can be obtained correctly as:

$\begin{array}{l}4x+7=x-2\text{writetheoriginalequation}\\ 4x-x+7=x-x-2\text{subtract}x\text{frombothsides}\\ 3x+7=0-2\text{simplify}\\ 3x+7-7=-2-7\text{subtract7frombothsides}\\ \text{3x}=-9\text{simplify}\\ \frac{3x}{3}=\frac{-9}{3}\text{divideeachby3}\\ x=-3\text{simplify}\end{array}$

So, the correct solution of the equation is $x=-3$