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Chapter 2: Problem 44

\(8 t+5=7 t\)

Short Answer

Expert verified
t = -5

Step by step solution

01

- Isolate the Variable

To isolate the variable t, begin by subtracting 7t from both sides of the equation to combine like terms. This gives us: 8t + 5 - 7t = 7t - 7ten 7t +
02

- Simplify the Equation

Simplify the left side of the equation by combining the terms that include t: 8t - 7t + 5 = 0. This simplifies to t + 5 = 0.
03

- Solve for t

To solve for t, subtract 5 from both sides of the equation. This will isolate t: t + 5 - 5 = 0 - 5.t = -5.

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Key Concepts

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

Isolating Variables
When solving a linear equation like the one given, our goal is to find the value of the variable. Here, we need to find the value of 饾憽. First, we need to isolate 饾憽 on one side of the equation. The equation we start with is: 8饾憽 + 5 = 7饾憽. To isolate 饾憽, we want all the terms containing 饾憽 on one side and constants on the other. We can do this by subtracting 7饾憽 from both sides. This gives us: 8饾憽 + 5 - 7饾憽 = 7饾憽 - 7饾憽, simplifying to: 饾憽 + 5 = 0.
Now 饾憽 is isolated on one side and we are ready to solve for it in the following steps.
Combining Like Terms
Combining like terms is an essential step in simplifying equations. Like terms are terms that contain the same variables raised to the same power. For the equation 8饾憽 + 5 - 7饾憽 = 0, we combine the 饾憽 terms by performing the subtraction.
On the left-hand side of the equation, we have 8饾憽 and -7饾憽. When combining these terms, we get 饾憽 (since 8饾憽 - 7饾憽 = 饾憽). Now, our equation looks like this: 饾憽 + 5 = 0.
By combining like terms, we鈥檝e simplified the equation and are one step closer to solving for 饾憽.
Simplifying Equations
Simplifying equations involves breaking down complex expressions into simpler ones to more easily find the solution. Once we have isolated the variable and combined like terms, our equation is: 饾憽 + 5 = 0.
The next step is to solve for 饾憽. To do this, we need to isolate 饾憽 completely. Subtract 5 from both sides of the equation: 饾憽 + 5 - 5 = 0 - 5, which simplifies to: 饾憽 = -5.
Now, we have found the value of 饾憽 that satisfies the original equation: 饾憽 = -5. This process of simplifying lets us solve linear equations step-by-step, making complex problems more manageable.

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Most popular questions from this chapter

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