Problem 101 Solve each equation. $$ 2 t+... [FREE SOLUTION]

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Chapter 5: Problem 101

Solve each equation. $$ 2 t+10=0 $$

Short Answer

Expert verified

t = -5

Step by step solution

Isolate the linear term

To isolate the linear term, subtract 10 from both sides of the equation: \[ 2t + 10 - 10 = 0 - 10 \]

Simplify the equation

Simplify the equation to obtain: \[ 2t = -10 \]

Solve for the variable

Divide both sides of the equation by 2 to solve for $ t $: \[ t = \frac{-10}{2} \]Simplifying this gives: \[ t = -5 \]

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Key Concepts

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

Isolating the Variable

To solve linear equations, the first important step is to isolate the variable you want to solve for. In our example, the equation is \[2t + 10 = 0\]. The variable here is \[t\].
To isolate \[t\], you need to remove any other numbers or terms that are adding or subtracting from it.
In this case, you subtract 10 from both sides of the equation to get the term with \[t\] alone on one side: \[2t + 10 - 10 = 0 - 10\].
This simplifies to: \[2t = -10\].
By isolating the variable, you are focusing directly on finding its value.

Simplifying Equations

Once you've successfully isolated the variable, the next major concept is simplifying the equation. Simplifying means making the equation as simple as possible to clearly see the relationship between the terms.
In the isolated equation \[2t = -10\], the next step is to make \[t\] stand alone.
You do this by dividing both sides of the equation by 2. This step is crucial because it tells us how \[t\] directly relates to the numbers in the problem.
So, \[2t / 2 = -10 / 2\] simplifies down to: \[t = -5\].
When you simplify equations, you break down complex relationships into simpler, more understandable parts.

Basic Algebra

Basic algebra is all about understanding and manipulating simple equations to find unknown values. The steps to solve equations generally follow a standard pattern:
Start by identifying the variable you need to solve for, then rearrange the equation to isolate that variable.
In the exercise given, the variable is \[t\], and through a series of logical steps, you isolate and solve for it.
Understanding these basic steps lays a strong foundation for more complex algebraic concepts you may encounter later on:

You may need to add, subtract, multiply, or divide both sides of the equation.
Always perform the same operation on both sides to keep the equation balanced.
Remember to simplify the equation at every step to make it easier to solve.

Basic algebra simplifies real-world problems, making them much easier to solve!

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91影视

Solve each equation. $$ 2 t+10=0 $$

Short Answer

Step by step solution

Isolate the linear term

Simplify the equation

Solve for the variable

Key Concepts

Isolating the Variable

Simplifying Equations

Basic Algebra

One App. One Place for Learning.

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