Solve For { J $} : : : { 119 + 11 = -3 - 7(5j - 9) \}

$$$$

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Introduction

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In this article, we will be solving a linear equation involving a variable $j$. The equation is given as $119 + 11 = -3 - 7(5j - 9)$. Our goal is to isolate the variable $j$ and find its value. We will use basic algebraic operations to simplify the equation and solve for $j$.

Step 1: Simplify the Left Side of the Equation

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The left side of the equation is $119 + 11$. We can simplify this by adding the two numbers together.

$$119 + 11 = 130$$

So, the equation becomes:

$$130 = -3 - 7(5j - 9)$$

Step 2: Distribute the Negative Sign

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The next step is to distribute the negative sign to the terms inside the parentheses.

$$-3 - 7(5j - 9) = -3 - 35j + 63$$

Now, the equation becomes:

$$130 = -3 - 35j + 63$$

Step 3: Combine Like Terms

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We can combine the constant terms on the right side of the equation.

$$-3 + 63 = 60$$

So, the equation becomes:

$$130 = 60 - 35j$$

Step 4: Isolate the Variable $j$

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To isolate the variable $j$, we need to get all the terms involving $j$ on one side of the equation. We can do this by subtracting 60 from both sides of the equation.

$$130 - 60 = -35j$$

This simplifies to:

$$70 = -35j$$

Step 5: Solve for $j$

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Finally, we can solve for $j$ by dividing both sides of the equation by -35.

$$\frac{70}{-35} = j$$

This simplifies to:

$$-2 = j$$

Conclusion

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In this article, we solved a linear equation involving a variable $j$. We used basic algebraic operations to simplify the equation and isolate the variable $j$. The final solution is $j = -2$.

Tips and Tricks

• When solving linear equations, it's essential to follow the order of operations (PEMDAS) to ensure that you're performing the operations in the correct order.
• When distributing a negative sign, remember to change the sign of each term inside the parentheses.
• When combining like terms, make sure to combine the constant terms separately from the terms involving the variable.

Real-World Applications

Linear equations like the one we solved in this article have many real-world applications. For example, they can be used to model population growth, chemical reactions, and electrical circuits. In finance, linear equations can be used to calculate interest rates and investment returns.

Further Reading

If you're interested in learning more about linear equations and algebra, here are some additional resources:

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Wolfram Alpha: Linear Equations

Final Answer

The final answer is $\boxed{-2}$.

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Introduction

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In our previous article, we solved a linear equation involving a variable $j$. In this article, we will answer some frequently asked questions about solving linear equations.

Q: What is a linear equation?

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A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: How do I solve a linear equation?

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To solve a linear equation, you need to isolate the variable on one side of the equation. You can do this by using basic algebraic operations such as addition, subtraction, multiplication, and division.

Q: What is the order of operations?

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The order of operations is a set of rules that tells you which operations to perform first when solving an equation. The order of operations 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 distribute a negative sign?

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When distributing a negative sign, you need to change the sign of each term inside the parentheses. For example, if you have the equation $-3(2x + 4)$, you would distribute the negative sign as follows:

$$-3(2x + 4) = -6x - 12$$

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

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A linear equation is an equation in which the highest power of the variable(s) is 1. A quadratic equation, on the other hand, is an equation in which the highest power of the variable(s) is 2. For example, the equation $x^2 + 4x + 4 = 0$ is a quadratic equation, while the equation $2x + 3 = 5$ is a linear equation.

Q: Can I use a calculator to solve a linear equation?

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Yes, you can use a calculator to solve a linear equation. However, it's always a good idea to check your work by plugging the solution back into the original equation.

Q: What are some real-world applications of linear equations?

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Linear equations have many real-world applications, including:

• Modeling population growth
• Calculating interest rates and investment returns
• Solving problems involving electrical circuits
• Determining the cost of goods and services

Q: Where can I learn more about linear equations?

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If you're interested in learning more about linear equations, here are some additional resources:

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Wolfram Alpha: Linear Equations
• Your local library or bookstore: There are many books and textbooks available on linear equations and algebra.

Q: What are some common mistakes to avoid when solving linear equations?

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Some common mistakes to avoid when solving linear equations include:

• Forgetting to distribute a negative sign
• Not following the order of operations
• Not checking your work by plugging the solution back into the original equation
• Not using a calculator to check your work

Conclusion

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In this article, we answered some frequently asked questions about solving linear equations. We hope that this article has been helpful in clarifying any confusion you may have had about linear equations. If you have any further questions, please don't hesitate to ask.

Final Answer

The final answer is $\boxed{0}$.