Rania solves the equation below by first squaring both sides of the equation.

-5=

3x - 7

What extraneous solution does Rania obtain?

The extraneous solution is 4.

Step-by-step explanation:

First, let us calculate the value of 'x' without squaring both side of the expression. This is illustrated below:

-5 = 3x - 7

Collect like terms

-5 + 7 = 3x

2 = 3x

Divide both side by 3

x = 2/3.

Now, let us calculate the value of 'x' by squaring both side of the expression. This is illustrated below:

(-5) ^2 = (3x - 7) ^2

25 = (3x - 7) (3x - 7)

25 = 9x^2 - 21x - 21x + 49

9x^2 - 42x + 49 - 25 = 0

9x^2 - 42x + 24 = 0

Solving by factorisation:

Multiply the first term i. e 9x^2 and 3rd term i. e 24 together. The result is 216x^2.

Next, we shall obtain two factors of 216x^2 such that when we add them together, it will give the 2nd term i. e - 42x in the equation. These factors are: - 6x and - 36x

Now we can write the above equation as:

9x^2 - 42x + 24 = 0

9x^2 - 6x - 36x + 24 = 0

3x (3x - 2) - 12 (3x - 2) = 0

(3x - 12) (3x - 2) = 0

3x - 12 = 0 or 3x - 2 = 0

3x = 12 or 3x = 2

x = 12/3 or x = 2/3

x = 4 or 2/3.

We can see that when we solve the question without squaring both side, the value of x is 2/3. But when we solve by squaring both side, the value of x are 4 and 2/3.

Therefore, the extraneous solution to the question is 4.