Question

How do you evaluate the expression $3a + 2b$ for $a = 1$ and $b = - 2$?

Answer 1

Hint: We need to evaluate the given algebraic expression. To do so, we simply substitute the values of the respective variables given in the question. After substitution, we solve the expression accordingly and get our required answer.

Complete step-by-step solution:
In order to evaluate the given expression, we simply need to substitute the values of the given variables in the expression,
Here the expression is given as: $3a + 2b$
There are two variables given here: $a$ and $b$
The value of $a$ is given as $1$ and the value of $b$ is given as $ - 2$
Placing in the above expression, we find:
$ \Rightarrow 3\left( 1 \right) + 2\left( { - 2} \right)$
On multiplying and simplifying, we get:
$ \Rightarrow 3 - 4 = - 1$
Thus, we have our required answer

Note: Evaluating an algebraic equation simply means to find its numerical value by substituting the values of each variable. Such algebraic expressions are easy to evaluate but care must be taken in substituting the correct sign and multiplying the equations. These expressions can be binomials, trinomials or polynomials.
Evaluating such equations is the basis of solving any complex algebraic equation. We need to be well versed with solving such numerical problems so that we can solve any other algebraic question with ease.
Let us take another expression as an example to show evaluation of algebraic expressions:
Let the expression be: $ - 4a + 5b - 6{c^2}$ for $a = 2,b = 7$ and $c = 3$
There are three variable given here: $a$,$b$ and $c$
The value of $a$ is given as $2$ , the value of $b$ is given as $7$ and the value of $c$ is given as $3$
Placing in the above expression, we find:
$ \Rightarrow - 4\left( 2 \right) + 5\left( 7 \right) - 6{\left( 3 \right)^2}$
On multiplying and simplifying, we get:
$ \Rightarrow - 8 + 35 - 54 = - 27$
Thus, we have our required answer.