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Chapter 3: Q9. (page 133)

Describe and correct the error in solving the equation

4x + 7 = x 鈥� 2

Short Answer

Expert verified

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

01

Step-1 – Given

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

02

Step-2 – To determine

We have to describe and correct the error..

03

Step-3 – Calculation

The provided solution of the equation is:

4x+7=x鈭�24x+7鈭�4x=x鈭�2鈭�4x7=3x鈭�27+2=3x鈭�2+29=3x3=x

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

The solution can be obtained correctly as:

4x+7=x鈭�2writetheoriginalequation4x鈭�x+7=x鈭�x鈭�2subtractxfrombothsides3x+7=0鈭�2simplify3x+7鈭�7=鈭�2鈭�7subtract7frombothsides3x=鈭�9simplify3x3=鈭�93divideeachby3x=鈭�3simplify

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

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