Question

How do you evaluate the expression for \[x = - 2\], \[y = 3\], \[z = - 4\,\,\] given \[7x - 2y - 8z?\]

Answer 1

Hint: This is a simple question of substitution. The values of the variables are given and an expression involving those variables is given. Just substitute the values given in the given expression and simplify.

Complete step by step answer:
The given expression is \[7x - 2y - 8z\]
If one closely observes, the expression involves some constants (their values can never be changed) and three variables. The values of these variables have to be found to make this into an expression containing only constants that could be further simplified. The variables involved in the equation are\[x\], \[y\] and \[z\] .
Now, in the question it is also given that \[x = - 2\], \[y = 3\] and\[z = - 4\,\,\]. This means the values of the variables are already given in the question, we don’t have to find these values.
Just by simply putting these values in the expression, we would be able to simplify the given expression.
So, substituting the values we get
\[
  7\, \times \,\underbrace x_ \downarrow - 2 \times \underbrace y_ \downarrow - 8 \times \,\,\underbrace z_ \downarrow \\
  7( - 2) - 2(3) - 8( - 4) \\
\]
Opening the brackets we get
\[ = - 14 - 6 + 32\]
By simplifications, we get
\[ = 12\]

Note:
A variable is a quantity whose value can be changed in the question. It is denoted by alphabets. Usually, they are used to indicate the quantities that are missing or are to be found. Constants are the digits whose value can never be changed in any question or situation.
\[\left( - \right) \times \left( - \right) = \left( + \right)\]
\[\left( - \right) \times \left( + \right) = \left( - \right)\]
\[\left( + \right) \times \left( - \right) = \left( - \right)\]
\[\left( + \right) \times \left( + \right) = \left( + \right)\]
Another property of integers used is while opening the brackets. Following rules are followed while opening the brackets.
If there is no operator in between the bracket and a digit, the operator assumed is always multiplication. It is necessary to keep in mind the signs of the while opening and closing the brackets.
In case of multiple operators in an expression, there is confusion about which operator should be solved first. In such a situation, follow BODMAS i.e. (Brackets followed by or followed by division then multiplication then addition and in the last subtraction).