Question

Simplify the expression and find its value if x = 3, a = –1 and b = –2.
10 – 3b – 4 – 5b

Answer 1

Hint: Assume the given expression as ‘E’. Now, group the terms containing the variable ‘b’ together while grouping the constant terms together. Take ‘b’ common from the terms containing the variable b and write their coefficients in brackets. Use simple arithmetic operations (addition and subtraction) to simplify the expression. Once the expression is simplified substitute the value of b = –2 to get the answer.

Complete step by step answer:
Here we have been provided with the expression 10 – 3b – 4 – 5 b and we are asked to simplify it and then find its value at x = 3, a = –1 and b = –2. Let us assume the given expression as E, so we have,
$\Rightarrow $ E = 10 – 3b – 4 – 5b
In the above expression we can see that there are four terms in which two of them contain the variable ‘b’ and two of them are constants, so we have to group the terms containing the variable ‘b’ together and the constant terms together to simplify it. So we have on grouping,
$\Rightarrow $ E = (10 – 4) + (–3b – 5b)
Taking ‘–b’ common from the last two terms in bracket we get,
$\Rightarrow $ E = (10 – 4) – b (3 + 5)
Therefore on simplifying using simple addition and subtraction we get,
$\Rightarrow $ E = 6 – 8b
Now, we can see that the above expression depends only on the value of b and not x and a, so the value of the expression will have no effect for the given values of x and a. Therefore substituting b = –2 we get,
$\Rightarrow $ E = $6-8\left( -2 \right)$
$\Rightarrow $ E = 6 + 16
$\therefore $ E = 22
Hence, the value of the given expression is 22.

Note: you can also find the value of the expression by first substituting the value of b in the given expression and then simplifying but in the question we have been told to simplify the equation first and then find the value. If any variable does not alter the value of a function then the function is said to be independent of that variable otherwise it is said to be dependent on that variable.