Problem 11 Solve. $$ \frac{-t}{5}=1 $... [FREE SOLUTION]

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Chapter 15: Problem 11

Solve. $$ \frac{-t}{5}=1 $$

Short Answer

Expert verified

t = -5

Step by step solution

- Understand the Equation

The given equation is $\frac{-t}{5} = 1$. It means that when $ -t $ is divided by 5, the result is 1.

- Eliminate the Fraction

To isolate $ t $, first get rid of the fraction by multiplying both sides of the equation by 5: \[ 5 \times \frac{-t}{5} = 1 \times 5 \] This simplifies to: \[ -t = 5 \]

- Solve for t

Now, solve for $ t $ by multiplying both sides by -1 to isolate $ t $: \[ -1 \times -t = 5 \times -1 \] This simplifies to: \[ t = -5 \]

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Key Concepts

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

Algebra

Algebra is a branch of mathematics that uses symbols and letters to represent numbers and quantities in formulas and equations. In algebra, we work with variables - symbols that can stand in for unknown values. By manipulating these variables according to specific rules, we can solve equations and find the values of unknowns.

For example, in the equation $\frac{-t}{5} = 1$, $-t$ represents an unknown value, and we aim to find the value of $-t$ that makes the equation true. Algebraic manipulation helps us to solve for this variable step by step.

Isolating Variables

Isolating the variable means to get the variable alone on one side of the equation. This allows us to solve for that variable. To isolate a variable, we use operations that 'undo' what has been done to the variable.

Let's look at the equation $\frac{-t}{5} = 1$. Our goal is to isolate \[ t \]. To do this:

First, multiply both sides by 5 to eliminate the fraction: \[ 5 \times \frac{-t}{5} = 1 \times 5 \]
This simplifies to \[ -t = 5 \], which means we have succeeded in eliminating the fraction and simplified the equation.
Next, multiply both sides by -1 to solve for \[ t \]: \[ -1 \times -t = 5 \times -1 \]
This yields \[ t = -5 \]. Now we know that \[ t \] equals -5 when the equation is true.

Multiplication Property of Equality

The Multiplication Property of Equality states that if you multiply both sides of an equation by the same nonzero number, the two sides remain equal. This is a crucial property when it comes to solving equations.

In our example, the equation $\frac{-t}{5} = 1$ can be manipulated using this property:

We multiplied both sides by 5 to eliminate the fraction: \[ 5 \times \frac{-t}{5} = 1 \times 5 \]
This gave us \[ -t = 5 \].
Next, to isolate \[ t \], we used the property again: multiplying both sides by -1 results in \[ -1 \times -t = 5 \times -1 \], simplifying to \[ t = -5 \].
Thus, the Multiplication Property of Equality helps us to systematically solve for the variable by ensuring we perform equivalent operations on both sides of the equation.

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91影视

Solve. $$ \frac{-t}{5}=1 $$

Short Answer

Step by step solution

- Understand the Equation

- Eliminate the Fraction

- Solve for t

Key Concepts

Algebra

Isolating Variables

Multiplication Property of Equality

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