Problem 16 Solve. $$ 12=5 y-18 $$... [FREE SOLUTION]

Chapter 15: Problem 16

Solve. $$ 12=5 y-18 $$

Short Answer

Expert verified

The value of $y$ is 6.

Step by step solution

Isolate the variable term

The equation given is $12 = 5y - 18$. First, add 18 to both sides of the equation to isolate the variable term ($5y$) on one side. \[12 + 18 = 5y - 18 + 18\]This simplifies to:\[30 = 5y\]

Solve for the variable

Now, divide both sides of the equation by 5 to solve for $y$. \[\frac{30}{5} = \frac{5y}{5}\]This simplifies to:\[y = 6\]

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Key Concepts

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

Isolate the Variable

Isolating the variable is the key to solving any linear equation. The main goal here is to have the variable (in our case, 'y') on one side of the equation by itself. From the exercise, we start with the equation: \[12 = 5y - 18\] To isolate '5y', we need to remove the constant on the same side as 'y'. We do this by performing the opposite operation. In this equation, we add 18 to both sides: \[12 + 18 = 5y - 18 + 18\] This simplifies to: \[30 = 5y\] By adding 18, we have successfully isolated the term '5y' on one side of the equation.

Equation Simplification

Equation simplification is essential. Once the variable term is isolated, make the equation simpler to solve. In our example, we simplified it by combining like terms. Let's revisit the modified equation: \[30 = 5y\] Here, the equation is quite simple, but let鈥檚 understand what it means to simplify:

First, make sure all like terms are combined (e.g., constants with constants, variables with variables).
Next, get the variable term as straightforward as possible, like '5y' on one side.

Now the equation is ready for the final step, making the variable stand alone.

Division in Algebra

Division in algebra is used to isolate the variable when it's multiplied by a coefficient. Having simplified our equation to: \[30 = 5y\] We want 'y' by itself, so we do the opposite of multiplication, which is division. We divide both sides of the equation by 5: \[\frac{30}{5} = \frac{5y}{5}\] This simplifies to: \[y = 6\] When we divide both sides by 5, we make 'y' stand alone.

This helps us solve for the variable.
Division undoes the multiplication by the coefficient (5 in this case).

Thus, we've found the value of 'y' in a simple and systematic way.

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91影视

Solve. $$ 12=5 y-18 $$

Short Answer

Step by step solution

Isolate the variable term

Solve for the variable

Key Concepts

Isolate the Variable

Equation Simplification

Division in Algebra

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