Question

What is the value of w in the equation \[\dfrac{1}{2}w + 7 = 2w - 2\]?

Answer 1

Hint: In this question, we have to simplify the given expression and find out the value of w.
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 need to move the terms with w in the left hand side and the constant terms in the right hand side. By simplifying this, we will get the required solution.

Complete step by step solution:
It is given that, \[\dfrac{1}{2}w + 7 = 2w - 2\].
We need to simplify the given equation\[\dfrac{1}{2}w + 7 = 2w - 2\] and find out the value of w.
To simplify the given equation, we need to move the terms involved in w in the left hand side and the constant term in the right hand side.
Following the above, we will get,
\[\dfrac{1}{2}w + 7 = 2w - 2\]
i.e.\[2w - \dfrac{1}{2}w = 7 + 2\]
Simplifying we get,
\[\dfrac{{4 - 1}}{2}w = 9\]
Or,\[\dfrac{3}{2}w = 9\]
Or,\[w = 9 \times \dfrac{2}{3}\]
Or,\[w = 6\]
Therefore, we get the value of w is \[6\].

Note: Algebraic operation:
In mathematics, a basic algebraic operation is any one of the common operations of arithmetic, which include addition, subtraction, 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. If you calculate them in the wrong order, you can get a wrong answer.