Question

How do you write the expression for the product of 8 and a number x increased by 10?

Answer 1

In algebra, an unknown variable quantity is represented by an alphabet. Just like the relationship between the specific words is conveyed by a statement, the relation between the unknown quantities is conveyed by algebraic equations, algebra helps in converting a mathematical statement into an equation. In the question, we are given a mathematical statement where a number “x” is the unknown quantity, so we will express the given statement as an algebraic expression using the information given above.

Complete step-by-step solution:
Let there be a number $“x”$.
The expression can be written in two ways as the statement is unclear.
If we read the statement as the product of 8 and a number “x”, increase by 10, we mean that 8 times x is added to 10 –
$8x+10$
But if we read the statement as the product of 8, and a number “x” increased by 10, we mean that 8 times the sum of x and 10 –
$8(x+10)$
Hence the expression for the product of 8 and a number x increased by 10 is either 8x+10 or 8(x+10).

Note: To define more generalized terms, we use algebra. For example in an arithmetic progression, we need an expression for finding out any term of the A.P. and also the sum of the A.P. so we use the definition of A.P. to find a more generalized expression. We can find many more examples of algebra used in various branches of mathematics.