91Ó°ÊÓ

When solving linear equations, our first goal is to isolate the variable. This means we need to get the variable alone on one side of the equation. In the given exercise, the equation is:
\( 14w + 5 = 117 \)
To do this, we need to move any constants (numbers that do not contain the variable) to the other side. This process involves basic arithmetic operations like adding, subtracting, multiplying, or dividing.
Start with moving constants away from the variable. In this case, the constant 5 is added to 14w. By subtracting 5 from both sides, we keep the equation balanced while moving closer to having the variable by itself.
For example,
\( 14w + 5 - 5 = 117 - 5 \)
This leaves us with:
\( 14w = 112 \)

Subtracting constants is an essential step in solving linear equations. This operation helps to simplify the equation and isolate the variable term. Think of constants as numbers that can be moved across the equation.
In our example:
Firstly subtract 5 from both sides since 5 is added to the term with the variable:
\( 14w + 5 - 5 = 117 - 5 \)
We subtract 5 from both sides of the equation. This operation cancels out the +5 on the left side, reducing the equation to:
\( 14w = 112 \)
When you subtract the same value from both sides, you maintain equality. It’s like balance scales – whatever you take from one side, you must also take from the other to keep it balanced.

The final step involves dividing coefficients. A coefficient is the number multiplied by the variable. In our exercise, 14 is the coefficient of w in the equation:
\( 14w = 112 \)
To isolate the variable w, we need to divide both sides by the coefficient 14:
\( \frac{14w}{14} = \frac{112}{14} \)
This simplifies to:
\( w = 8 \)
Dividing both sides by the same number doesn’t change the equality of the equation. It merely simplifies the equation, making it easier to see the value of the variable.
Through this process, we find that w equals 8. This means the value of w that satisfies the original equation \( 14w + 5 = 117 \) is 8.