Question

How do you simplify $3(x + 2) + 5x$ ?

Answer 1

Hint: In this question, we have to simplify the algebraic expression given to us; the algebraic expression is in terms of x. The given expression is called an algebraic expression because it is a combination of numerical values and alphabets. The alphabets in an algebraic expression represent some unknown quantity, so “x” represents some unknown variable quantity in the given expression. The alphabets and numerical values are linked to each other by some arithmetic operations like addition, subtraction, multiplication and division. We will simplify the given algebraic expression by using the distributive property then we will apply the given arithmetic operations to further simplify it.

Complete step-by-step solution:
We have to simplify $3(x + 2) + 5x$
On applying the distributive property –
$3(x + 2) + 5x = (3 \times x) + (3 \times 2) + 5x$
$5x$ represents the product of 5 and x, so $3 \times x = 3x$
So, we get –
$3(x + 2) + 5x = 3x + 6 + 5x$
Now, we will group the similar terms, that is, we will write the terms containing “x” side by side –
$3(x + 2) + 5x = 3x + 5x + 6$
We will again apply the distributive property and take “x” common –
$3(x + 2) + 5x = x(3 + 5) + 6$
Now, we will apply the arithmetic operation in the brackets –
$3(x + 2) + 5x = 8x + 6$
Hence the simplified form of $3(x + 2) + 5x$ is $8x + 6$ .

Note: The given algebraic expression is simplified using the distributive property. The distributive property states that the product of a number with the sum of two other numbers is equal to the product of that number with the first number plus the product of that number with the second number and vice versa, that is, $a(b + c) = ab + ac$ . We can also find the value of the unknown variable quantity with the help of an algebraic equation.