Solve For X X X . − 2 = − 7 X + 5 ( X + 2 -2 = -7x + 5(x + 2 − 2 = − 7 X + 5 ( X + 2 ]Simplify Your Answer As Much As Possible. X = X = X =

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Introduction

In mathematics, solving for a variable is a fundamental concept that involves isolating the variable on one side of the equation. In this article, we will focus on solving for xx in the given equation −2=−7x+5(x+2)-2 = -7x + 5(x + 2). We will simplify the equation step by step to find the value of xx.

Understanding the Equation

The given equation is −2=−7x+5(x+2)-2 = -7x + 5(x + 2). To solve for xx, we need to simplify the equation by combining like terms and isolating the variable xx.

Distributive Property

The first step in simplifying the equation is to apply the distributive property to the term 5(x+2)5(x + 2). The distributive property states that for any real numbers aa, bb, and cc, a(b+c)=ab+aca(b + c) = ab + ac. Applying this property to the term 5(x+2)5(x + 2), we get:

5(x+2)=5x+105(x + 2) = 5x + 10

Substituting the Simplified Term

Now that we have simplified the term 5(x+2)5(x + 2), we can substitute it back into the original equation:

−2=−7x+5x+10-2 = -7x + 5x + 10

Combining Like Terms

The next step is to combine like terms on the right-hand side of the equation. We can combine the terms −7x-7x and 5x5x to get:

−2=2x+10-2 = 2x + 10

Isolating the Variable

Now that we have combined like terms, we can isolate the variable xx by subtracting 1010 from both sides of the equation:

−2−10=2x-2 - 10 = 2x

−12=2x-12 = 2x

Solving for xx

Finally, we can solve for xx by dividing both sides of the equation by 22:

x=−122x = \frac{-12}{2}

x=−6x = -6

Conclusion

In this article, we solved for xx in the equation −2=−7x+5(x+2)-2 = -7x + 5(x + 2). We simplified the equation step by step by applying the distributive property, combining like terms, and isolating the variable xx. The final solution is x=−6x = -6.

Tips and Tricks

  • When solving for a variable, it's essential to simplify the equation by combining like terms and isolating the variable.
  • The distributive property is a powerful tool for simplifying equations.
  • When dividing both sides of an equation by a coefficient, make sure to divide the constant term by the same coefficient.

Frequently Asked Questions

  • Q: What is the distributive property? A: The distributive property is a mathematical concept that states that for any real numbers aa, bb, and cc, a(b+c)=ab+aca(b + c) = ab + ac.
  • Q: How do I combine like terms? A: To combine like terms, add or subtract the coefficients of the terms with the same variable.
  • Q: How do I isolate the variable? A: To isolate the variable, subtract or add the constant term to both sides of the equation.

Further Reading

References

Note: The references provided are for demonstration purposes only and may not be actual references.

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Introduction

In our previous article, we solved for xx in the equation −2=−7x+5(x+2)-2 = -7x + 5(x + 2). In this article, we will answer some frequently asked questions related to solving for xx.

Q&A

Q: What is the first step in solving for xx?

A: The first step in solving for xx is to simplify the equation by combining like terms and isolating the variable.

Q: How do I apply the distributive property?

A: To apply the distributive property, multiply the coefficient of the term by each term inside the parentheses.

Q: What is the difference between combining like terms and isolating the variable?

A: Combining like terms involves adding or subtracting the coefficients of the terms with the same variable, while isolating the variable involves subtracting or adding the constant term to both sides of the equation.

Q: How do I know which side of the equation to isolate the variable on?

A: Typically, you want to isolate the variable on the left-hand side of the equation. However, if the equation is more complex, you may need to isolate the variable on the right-hand side.

Q: What if I have a fraction on one side of the equation?

A: If you have a fraction on one side of the equation, you can multiply both sides of the equation by the denominator to eliminate the fraction.

Q: Can I use a calculator to solve for xx?

A: Yes, you can use a calculator to solve for xx. However, it's essential to understand the steps involved in solving for xx so that you can verify the solution.

Q: What if I get a negative value for xx?

A: If you get a negative value for xx, it means that the solution is not valid. You may need to re-examine your work and try again.

Q: Can I use the same steps to solve for xx in a quadratic equation?

A: No, the steps for solving for xx in a quadratic equation are different. You will need to use the quadratic formula or complete the square to solve for xx.

Tips and Tricks

  • Always simplify the equation before solving for xx.
  • Use the distributive property to simplify expressions with parentheses.
  • Combine like terms to make the equation easier to solve.
  • Isolate the variable on one side of the equation.
  • Use a calculator to verify your solution.

Frequently Asked Questions

  • Q: What is the distributive property? A: The distributive property is a mathematical concept that states that for any real numbers aa, bb, and cc, a(b+c)=ab+aca(b + c) = ab + ac.
  • Q: How do I combine like terms? A: To combine like terms, add or subtract the coefficients of the terms with the same variable.
  • Q: How do I isolate the variable? A: To isolate the variable, subtract or add the constant term to both sides of the equation.

Further Reading

References

Additional Resources

Note: The references provided are for demonstration purposes only and may not be actual references.