Question

How do you solve \[9\left( {3 - 2x} \right) = 2\left( {10 - 8x} \right)\]?

Answer 1

Hint: In this question, we have to solve the given equation.
To simplify a given problem we need to use the BODMAS rule.
Rule:
B→ Brackets first
O→ Orders (i.e. Powers and Square Roots, etc.)
DM→ Division and Multiplication (left-to-right)
AS→ Addition and Subtraction (left-to-right)
First we remove the bracket and for doing that we need to multiply the constant term with the first term within the bracket then put the negative sign and multiply it with the second term left side and right side of the equal sign. By simplifying this we will get the required solution.

Complete step by step solution:
It is given that, \[9\left( {3 - 2x} \right) = 2\left( {10 - 8x} \right)\].
We need to solve the equation \[9\left( {3 - 2x} \right) = 2\left( {10 - 8x} \right)\].
To simplify the given equation we need to follow the BODMAS rule. For that we have to remove the bracket first.
We will remove the bracket by multiplying the constant term with the first term within the bracket then putting the negative sign and multiply it with the second term left side and right side of the equal sign.
\[ \Rightarrow 9\left( {3 - 2x} \right) = 2\left( {10 - 8x} \right)\]
\[ \Rightarrow 9 \times 3 - 9 \times 2x = 2 \times 10 - 2 \times 8x\]
Now simplifying we get,
\[ \Rightarrow 27 - 18x = 20 - 16x\]
Therefore, \[18x - 16x = 27 - 20\].
\[ \Rightarrow 2x = 7\]
\[ \Rightarrow x = \dfrac{7}{2}\]

Hence solving \[9\left( {3 - 2x} \right) = 2\left( {10 - 8x} \right)\], we get \[x = \dfrac{7}{2}\].

Note: Algebraic operation:
In mathematics, a basic algebraic operation is any one of the common operations of arithmetic, which include addition, subtraction, and multiplication, division, raising to an integer power, and taking roots (fractional power).
To simplify algebraic expressions we will consider highest power first then less the powers accordingly and end it with the constant term.
“Operations” mean things like add, subtract, multiply, divide, squaring, etc. If it isn’t a number it is probably an operation.
You need to always follow the BODMAS rule. Calculate them in the wrong order, and you can get a wrong answer.