Solve For W W W In The Equation: − 6 W + 8 ( W − 3 ) = − 38 -6w + 8(w - 3) = -38 − 6 W + 8 ( W − 3 ) = − 38 Simplify Your Answer As Much As Possible. W = W = W =

$$$$

Introduction

Solving linear equations is a fundamental concept in mathematics, and it is essential to understand how to simplify and solve these equations to find the value of the variable. In this article, we will focus on solving the equation $-6w + 8(w - 3) = -38$ to find the value of $w$. We will use algebraic techniques to simplify the equation and isolate the variable.

Understanding the Equation

The given equation is $-6w + 8(w - 3) = -38$. To solve for $w$, we need to simplify the equation and isolate the variable. The equation involves two terms with the variable $w$, and we need to combine like terms to simplify the equation.

Distributing the Coefficient

The first step in simplifying the equation is to distribute the coefficient $8$ to the terms inside the parentheses. This will give us:

$$-6w + 8w - 24 = -38$$

Combining Like Terms

Now that we have distributed the coefficient, we can combine like terms to simplify the equation. The like terms are the terms with the variable $w$, and we can combine them as follows:

$$2w - 24 = -38$$

Isolating the Variable

To isolate the variable $w$, we need to get rid of the constant term $-24$. We can do this by adding $24$ to both sides of the equation:

$$2w = -38 + 24$$

Simplifying the Equation

Now that we have added $24$ to both sides of the equation, we can simplify the right-hand side of the equation:

$$2w = -14$$

Solving for $w$

To solve for $w$, we need to isolate the variable by dividing both sides of the equation by $2$:

$$w = \frac{-14}{2}$$

Simplifying the Answer

Finally, we can simplify the answer by dividing $-14$ by $2$:

$$w = -7$$

Conclusion

In this article, we solved the equation $-6w + 8(w - 3) = -38$ to find the value of $w$. We used algebraic techniques to simplify the equation and isolate the variable. The final answer is $w = -7$.

Tips and Tricks

• When solving linear equations, it is essential to simplify the equation and isolate the variable.
• Use algebraic techniques such as distributing coefficients and combining like terms to simplify the equation.
• Be careful when adding or subtracting terms to both sides of the equation, as this can affect the value of the variable.

Frequently Asked Questions

• Q: What is the value of $w$ in the equation $-6w + 8(w - 3) = -38$? A: The value of $w$ is $-7$.
• Q: How do I simplify the equation $-6w + 8(w - 3) = -38$? A: To simplify the equation, you can distribute the coefficient $8$ to the terms inside the parentheses and combine like terms.
• Q: How do I isolate the variable $w$ in the equation $-6w + 8(w - 3) = -38$? A: To isolate the variable $w$, you can add or subtract terms to both sides of the equation to get rid of the constant term.

Related Topics

• Solving linear equations
• Algebraic techniques
• Distributing coefficients
• Combining like terms
• Isolating variables

References

• [1] Algebra textbook by Michael Artin
• [2] Linear equations tutorial by Khan Academy
• [3] Algebraic techniques tutorial by Mathway

Keywords

• Linear equations
• Algebraic techniques
• Distributing coefficients
• Combining like terms
• Isolating variables
• Solving equations
• Algebra
• Mathematics
  

Introduction

Solving linear equations is a fundamental concept in mathematics, and it is essential to understand how to simplify and solve these equations to find the value of the variable. In this article, we will answer some frequently asked questions about solving linear equations.

Q&A

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. For example, the equation $2x + 3 = 5$ is a linear equation.

Q: How do I simplify a linear equation?

A: To simplify a linear equation, you can use algebraic techniques such as distributing coefficients and combining like terms. For example, the equation $-6w + 8(w - 3) = -38$ can be simplified by distributing the coefficient $8$ to the terms inside the parentheses and combining like terms.

Q: How do I isolate the variable in a linear equation?

A: To isolate the variable in a linear equation, you can add or subtract terms to both sides of the equation to get rid of the constant term. For example, the equation $2w - 24 = -38$ can be solved by adding $24$ to both sides of the equation to get $2w = -14$.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1, while a quadratic equation is an equation in which the highest power of the variable is 2. For example, the equation $x^2 + 2x + 1 = 0$ is a quadratic equation.

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, you can multiply both sides of the equation by the least common multiple (LCM) of the denominators to eliminate the fractions. For example, the equation $\frac{1}{2}x + 3 = 5$ can be solved by multiplying both sides of the equation by 2 to get $x + 6 = 10$.

Q: What is the order of operations when solving a linear equation?

A: The order of operations when solving a linear equation is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I check my solution to a linear equation?

A: To check your solution to a linear equation, you can plug the solution back into the original equation and verify that it is true. For example, if you solve the equation $2x + 3 = 5$ and get $x = 1$, you can plug $x = 1$ back into the original equation to get $2(1) + 3 = 5$, which is true.

Tips and Tricks

• When solving linear equations, it is essential to simplify the equation and isolate the variable.
• Use algebraic techniques such as distributing coefficients and combining like terms to simplify the equation.
• Be careful when adding or subtracting terms to both sides of the equation, as this can affect the value of the variable.
• When solving linear equations with fractions, multiply both sides of the equation by the least common multiple (LCM) of the denominators to eliminate the fractions.

Frequently Asked Questions

• Q: What is the value of $x$ in the equation $2x + 3 = 5$? A: The value of $x$ is 1.
• Q: How do I simplify the equation $-6w + 8(w - 3) = -38$? A: To simplify the equation, you can distribute the coefficient $8$ to the terms inside the parentheses and combine like terms.
• Q: How do I isolate the variable $x$ in the equation $2x - 24 = -38$? A: To isolate the variable $x$, you can add $24$ to both sides of the equation to get $2x = -14$.

Related Topics

• Solving linear equations
• Algebraic techniques
• Distributing coefficients
• Combining like terms
• Isolating variables
• Solving equations
• Algebra
• Mathematics

References

• [1] Algebra textbook by Michael Artin
• [2] Linear equations tutorial by Khan Academy
• [3] Algebraic techniques tutorial by Mathway

Keywords

• Linear equations
• Algebraic techniques
• Distributing coefficients
• Combining like terms
• Isolating variables
• Solving equations
• Algebra
• Mathematics