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Chapter 4: Problem 17

Solve and check. $$x+10=-7$$

Short Answer

Expert verified
Question: Solve the equation x + 10 = -7 and check if the solution is correct. Answer: x = -17

Step by step solution

01

Identify the equation

The given equation is: $$x + 10 = -7$$ Our goal is to solve this equation for x.
02

Isolate the variable "x"

In order to isolate x, we need to get rid of the 10 on the left side of the equation. We can do this by subtracting 10 from both sides: $$x + 10 - 10 = -7 - 10$$ This simplifies to: $$x = -17$$
03

Check the solution

To check if the solution is correct, substitute the value of x back into the original equation: $$(-17) + 10 = -7$$ This simplifies to: $$-7 = -7$$ Since the equation is true, our solution of x = -17 is correct.

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Key Concepts

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

Isolate the Variable
In solving linear equations, the first core step is to isolate the variable. Isolating the variable refers to the process of manipulating the equation such that the variable we're solving for is on one side of the equation, and everything else is on the other side.

For example, consider the equation \(x + 10 = -7\). To isolate the variable \(x\), you must remove the number 10 that is added to it. This is done by doing the opposite operation: subtracting 10 from both sides. The equation becomes \(x + 10 - 10 = -7 - 10\), which simplifies to \(x = -17\). By performing the subtraction, we have successfully isolated the variable \(x\) and can now easily read its value.
Equation Solving Steps
To tackle any linear equation effectively, it's essential to follow a methodical set of steps. Start by carefully examining the given equation. Identify any operations performed on the variable and consider the inverse operations to undo those effects.

Here are the universal steps to solve linear equations:
  • Identify and write down the given equation.
  • Isolate the variable by performing inverse operations (addition/subtraction, multiplication/division).
  • Simplify the equation if necessary by combining like terms and reducing fractions.
  • Write down the solution, ensuring the variable is by itself on one side of the equals sign.

Following these steps ensures that you methodically solve the equation and reach the correct solution, while also setting a solid foundation for dealing with more complex algebraic problems.
Checking the Solution
After finding a solution to an equation, it鈥檚 critical to verify its accuracy. Checking your solution involves substituting the value back into the original equation and confirming that the equality holds true.

This practice not only helps you catch any potential errors, but it also reinforces your understanding of how the equations work. For the original exercise \(x + 10 = -7\), after identifying that \(x = -17\), you would replace \(x\) with -17 in the initial equation: \( (-17) + 10 = -7 \). Simplifying this gives you \( -7 = -7 \), which confirms that the solution is correct. Always remember to include this crucial step to validate your results.

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