Question

Solve $3(x + 6) + 2(x + 3) = 64$ for the value of $x$ .

Answer 1

Hint: In this question, we are given an equation that we have to solve for $x$. So, first ,we will simplify the left-hand side and then solve for $x$ . To solve these brackets, we will apply the distributive property of addition, since there is an addition sign only.
The distributive property over addition is given by $a \times \left( {b + c} \right) = a \times b + a \times c$ .

Complete step-by-step answer:
Given equation $3(x + 6) + 2(x + 3) = 64$ .
To solve the given equation for $x$ .
First write the given equation $3(x + 6) + 2(x + 3) = 64$ .
Now, using the distributive property of addition, we will solve the brackets.
So, on solving we get, $3 \times x + 3 \times 6 + 2 \times x + 2 \times 3 = 64$ , which gives, $3x + 18 + 2x + 6 = 64$ .
Now, solve the like terms on the right-hand side, we get, $5x + 24 = 64$ .
Now, since $24$ is being added on the left-hand side, so we will subtract $24$ on both sides, we get $5x + 24 - 24 = 64 - 24$ , which gives $5x = 40$ .
Now, $5$ is being multiplied on the left-hand side, so we will divide by $5$ on both sides so that we will get the coefficient of $x$ as $1$ , we get, $\dfrac{{5x}}{5} = \dfrac{{40}}{5}$ , which gives, $x = 8$ .
Hence, we get $x = 8$ , on solving $3(x + 6) + 2(x + 3) = 64$ .

Note: Like terms are referred to as the terms with the same variable and with the same power. For example: $4{x^2}$ and $7{x^2}$ are like terms whereas, $4{x^2}$ and $4x$ or $4{x^2}$ and $4xy$ are unlike terms.
One needs to know the basics of algebra very well to solve such equations.
To solve an equation with multiple operations, we must use the BODMAS rule to get the correct answer. ‘BODMAS’ means B- Brackets, O- Of, D- Division, M- Multiplication, A- Addition, S- Subtraction.