Solve For $w$.$-\frac{3}{5} W = 12$Simplify Your Answer As Much As Possible.

Mar 11, 2025 by ADMIN 81 views

$Solve for w: $-\frac{3}{5} w = 12$$

Understanding the Problem

To solve for w, we need to isolate the variable w on one side of the equation. The given equation is a linear equation, and we can use basic algebraic operations to solve for w.

Step 1: Multiply Both Sides by the Reciprocal of the Coefficient

The coefficient of w is -3/5. To get rid of the fraction, we can multiply both sides of the equation by the reciprocal of the coefficient, which is -5/3.

-\frac{3}{5} w = 12
\implies w = -12 \times \frac{5}{3}

Step 2: Simplify the Expression

Now, we can simplify the expression by multiplying -12 by 5 and then dividing the result by 3.

w = -12 \times \frac{5}{3}
\implies w = -60 \div 3
\implies w = -20

Conclusion

Therefore, the value of w is -20.

Checking the Solution

To check our solution, we can plug w = -20 back into the original equation and see if it's true.

-\frac{3}{5} w = 12
\implies -\frac{3}{5} (-20) = 12
\implies \frac{60}{5} = 12
\implies 12 = 12

Final Answer

The final answer is $\boxed{-20}$ .

Example Use Cases

Solving for w in the equation $\frac{2}{3} w = 15$
Finding the value of x in the equation $x - 2 = 7$

Tips and Tricks

When solving for a variable, always isolate the variable on one side of the equation.
Use basic algebraic operations such as addition, subtraction, multiplication, and division to solve for the variable.
Simplify expressions by combining like terms and canceling out common factors.

Frequently Asked Questions

Q: What is the value of w in the equation $-\frac{3}{5} w = 12$?

A: The value of w is -20.

Q: How do I solve for w in the equation $-\frac{3}{5} w = 12$?

A: To solve for w, you need to isolate the variable w on one side of the equation. You can do this by multiplying both sides of the equation by the reciprocal of the coefficient, which is -5/3.

Q: What is the reciprocal of the coefficient -3/5?

A: The reciprocal of the coefficient -3/5 is -5/3.

Q: How do I simplify the expression $-12 \times \frac{5}{3}$?

A: To simplify the expression, you can multiply -12 by 5 and then divide the result by 3.

Q: What is the final answer to the equation $-\frac{3}{5} w = 12$?

A: The final answer is $\boxed{-20}$ .

Q: How do I check my solution to the equation $-\frac{3}{5} w = 12$?

A: To check your solution, you can plug w = -20 back into the original equation and see if it's true.

Q: What are some related topics to solving for w in the equation $-\frac{3}{5} w = 12$?

A: Some related topics include solving linear equations, algebraic operations, and simplifying expressions.

Q: Can you provide an example of how to solve for x in the equation $x - 2 = 7$?

A: To solve for x, you can add 2 to both sides of the equation, resulting in x = 9.

Q: What are some tips and tricks for solving for variables in equations?

A: Some tips and tricks include always isolating the variable on one side of the equation, using basic algebraic operations such as addition, subtraction, multiplication, and division, and simplifying expressions by combining like terms and canceling out common factors.