The coordinates of points A (a) and B (b) are the roots of the equation. | x – 2 | = 7

| April 18, 2021 | education

The coordinates of points A (a) and B (b) are the roots of the equation. | x – 2 | = 7 Find the distance between points A and B.

Let’s solve the equation | х – 2 | = 7.

For x – 2> = 0, the expression | x – 2 | = x – 2, thus:

x – 2 = 7;

x = 9 – this root satisfies the condition x – 2> = 0, therefore it is a solution to the original modular equation.

For x – 2 <0, the expression | x – 2 | = – x + 2, thus:

– x + 2 = 7;

x = – 5 – this root satisfies the condition x – 2 <0, therefore it is a solution to the original modular equation.

By the condition of the problem, the roots of the modular equation are the coordinates of points A and B on the number line. The distance between them is equal to the modulus of the coordinate difference:

| – 5 – 2 | = | – 7 | = 7.

Answer: 7.



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