Below u, v, w and x represent different integers, where u = -4 and x ≠ 1. By using following equations, find each of the values:
u × v = u
x × w = w
u + x = w
a. v
b. w
c. x
Explain your reasoning using the properties of integers

Solution:

Let us use the properties of integers and multiplicative identity rules to find the value of u, v, w, x.

1. u × v = u and given that u = -4. Hence, -4 × v = -4 v = 1
2. x × w = w. It is given, x ≠ 1 So, x × w = w. This is possible only when w = 0.
3. As u + x = w, now put u = -4 and w = 0. So, -4 + x = 0 x = 4

✦ Try This: Find the value of v in the expression u × v = u if u = -18

To find the value of v in the expression u × v = u we will simply use properties of integers and will substitute u = -18 to get the required answer.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 1

NCERT Exemplar Class 7 Maths Chapter 1 Exercise Problem 127

Below u, v, w and x represent different integers, where u = –4 and x ≠ 1. By using the following equations, find each of the values: u × v = u, x × w = w, u + x = w, a. v, b. w, c. x. Explain your reasoning using the properties of integers

Summary:

After applying the properties of integers we examined that: a. u × v = u and given that u = -4. Hence, -4 × v = -4 v = 1 b. x × w = w. It is given, x ≠ 1 So, x × w = w. This is possible only when w = 0. c. As u + x = w, now put u = -4 and w = 0. So, -4 + x = 0 x = 4

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