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Chapter 2: Problem 36

Solve equation, and check your solution. \(-t=14\)

Short Answer

Expert verified
The solution is \(t = -14\).

Step by step solution

01

Isolate the variable

To isolate the variable on one side of the equation, divide both sides of the equation by \(-1\). This will remove the negative sign in front of \(t\). So, start with the equation: \(-t = 14\) Divide both sides by \(-1\): \[ t = \frac{14}{-1} \] Simplifies to: \[ t = -14 \]
02

Check the solution

To check your solution, substitute \(t = -14\) back into the original equation: \(-(-14) = 14\) Simplifies to: \[ 14 = 14 \] Since both sides of the equation are equal, the solution \(t = -14\) 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
When solving a linear equation, a key step is to isolate the variable you are solving for. This means you want to get the variable by itself on one side of the equation. In this example, the equation is \(-t = 14\). To isolate the variable \(t\), you need to remove the negative sign. You can do this by dividing both sides of the equation by \(-1\). When you divide both sides of \(-t = 14\) by \(-1\), it simplifies to: \[ t = \frac{14}{-1} \] which further simplifies to: \[ t = -14 \]. Now, the variable \(t\) is isolated, and you have found that \(t = -14\).
Checking solutions
After solving an equation, it's important to check your solution to make sure it is correct. To check your solution, substitute the value you found back into the original equation. For our example, we found \(t = -14\) so we substitute \(-14\) back into the original equation \(-t = 14\). That means we are actually calculating: \(-(-14) = 14\). Since \[ -(-14) = 14 \] simplifies to \[ 14 = 14 \], which is true, our solution \(t = -14\) is correct. This step ensures that you haven't made any mistakes in your calculations and that your solution satisfies the original equation.
Negative coefficients
Dealing with negative coefficients can sometimes be tricky. A coefficient is a number that multiplies a variable. In the equation \(-t = 14\), the negative sign in front of \(t\) makes \(-1\) the coefficient of \(t\). To handle this correctly, we need to 'flip' the negative sign by dividing both sides of the equation by \(-1\). Note that dividing or multiplying by \(-1\) changes the sign of the number. So for \(-t = 14\), dividing both sides by \(-1\) results in: \[ t = \frac{14}{-1} = -14 \]. This process is crucial when solving equations with negative coefficients, as it simplifies the equation and isolates the variable, letting you easily find the solution.

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