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Chapter 8: Problem 120

Solve the equation for the variable. $$25=-9 y+7$$

Short Answer

Expert verified
y = -2

Step by step solution

01

Isolate the Variable Term

Start by moving the constant on the right side of the equation to the left side. Subtract 7 from both sides of the equation: \[ 25 - 7 = -9y \]
02

Simplify the Equation

Simplify the left side of the equation to get: \[ 18 = -9y \]
03

Solve for the Variable

To isolate y, divide both sides of the equation by -9: \[ y = \frac{18}{-9} \]
04

Simplify the Result

Simplify the fraction to get the final answer: \[ y = -2 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolation of Variable
The first core concept in solving linear equations is isolating the variable. This means getting the variable term (in this case, the term with y) by itself on one side of the equation.
For the equation \( 25 = -9y + 7 \), start by moving the constant term, 7, to the other side of the equation.
This process involves subtracting 7 from both sides:
\[ 25 - 7 = -9y \]
This operation eliminates the constant on the right side, leaving the variable term isolated.
Simplifying Equations
Once the variable term is isolated, the next step is to simplify the equation. Simplifying means reducing the equation to its simplest form.
After isolating the variable term in our example, we have:
\[ 25 - 7 = -9y \]
Simplify the left side by executing the subtraction:
\[ 18 = -9y \]
Now, the equation is easier to work with. The left side is a single number, and the right side still contains the term with the variable y.
Solving for a Variable
Finally, we solve for the variable. This step involves getting the variable y by itself on one side of the equation.
From the simplified equation:
\[ 18 = -9y \]
To isolate y, divide both sides by the coefficient of y, which is -9:
\[ y = \frac{18}{-9} \]
Finish by simplifying the fraction to get the final answer:
\[ y = -2 \]
Now you've successfully solved the equation for y. This process can be applied to any linear equation you encounter.

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