What values can the module x-7 take if the module x-4 = 6.

We have the expression:

| x – 4 | = 6.

Find the values that the expression | x – 7 | can take.

The modulus of a number is its absolute value. In simple words, modulus is the distance from a number to zero on the number axis. The modulus value is always a non-negative number.

We get:

| x – 4 | = 6;

x – 4 = 6 or

x – 4 = -6;

x = 10 or x = -2.

We substitute the obtained values into the sign of the module, which we need to find:

1) If x = 10, then:

| x – 7 | = | 10 – 7 | = 3.

2) If x = -2, then:

| x – 7 | = | -2 – 7 | = 9.