Problem 21 Solve each equation, and check y... [FREE SOLUTION]

Chapter 2: Problem 21

Solve each equation, and check your solution. $$ -4=x-14 $$

Short Answer

Expert verified

x = 10

Step by step solution

Isolate the variable

Start by isolating the variable on one side of the equation. Add 14 to both sides of the equation to cancel out the $-14$ on the right-hand side.

Simplify both sides

When we add 14 to both sides, the equation becomes: $-4 + 14 = x - 14 + 14$. Simplifying this, we get $10 = x$.

Check the solution

To ensure the solution \x = 10\ is correct, substitute 10 back into the original equation. $-4 = 10 - 14$. Simplifying, we get $-4 = -4$, confirming that the solution 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, one of the first and most crucial steps is to isolate the variable. This means you need to move all terms containing the variable to one side of the equation and everything else to the other side. For the equation $-4 = x - 14$, our goal is to get $x$ by itself on one side. To do this, add $14$ to both sides: $-4 + 14 = x - 14 + 14$. This allows you to simplify your equation to \10 = x\. Now, you have successfully isolated the variable.

Check solution

After solving for the variable, it鈥檚 important to check your solution to ensure it鈥檚 correct. This helps confirm that the manipulations you performed are accurate. To check the solution $x = 10$, substitute 10 back into the original equation. The original equation is $-4 = x - 14$. By placing 10 where $x$ is, you get $-4 = 10 - 14$. Simplify the right side: $-4$, which matches the left side of the equation. When both sides are the same, your solution is verified and correct.

Simplify equations

Simplifying equations involves combining like terms and performing basic arithmetic operations to make the equation easier to solve. In our example, once we added $14$ to both sides: $-4 + 14 = x - 14 + 14$, you simplify the left side to get \10\. The right side simplifies to just $x$, giving us the simplified equation \10 = x\. Remember, simplifying your equations at each step makes solving them much more manageable and increases accuracy. Breaking down each part systematically prevents mistakes and helps you understand each operation.

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91影视

Solve each equation, and check your solution. $$ -4=x-14 $$

Short Answer

Step by step solution

Isolate the variable

Simplify both sides

Check the solution

Key Concepts

Isolate the variable

Check solution

Simplify equations

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