Problem 704 In the following exercises, solv... [FREE SOLUTION]

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Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 5: Problem 704

In the following exercises, solve. $$ 1.94=a-2.6 $$

Short Answer

Expert verified

a = 4.54

Step by step solution

- Identify the Equation

The given equation is: 1.94 = a - 2.6

- Add 2.6 to Both Sides

To isolate the variable 'a', add 2.6 to both sides of the equation. 1.94 + 2.6 = a - 2.6 + 2.6

- Simplify the Equation

Simplify both sides. On the right side, the -2.6 and +2.6 cancel each other out. 1.94 + 2.6 = a 4.54 = a

- Write the Solution

The value of 'a' has been found. a = 4.54

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Key Concepts

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

isolating the variable

Isolating the variable is a core concept in solving linear equations. The goal is to get the variable by itself on one side of the equation.
In the problem given, we are solving for 'a' in the equation: 1.94 = a - 2.6.
To isolate 'a', we need to remove any other numbers from its side of the equation. This involves performing the same operation on both sides of the equation.

For example, we add 2.6 to both sides to get rid of the -2.6 on the right:
1.94 + 2.6 = a - 2.6 + 2.6.
The -2.6 and +2.6 cancel each other, leaving us with only 'a' on the right.
This step is crucial because it isolates the variable, making it possible to determine its value.

balancing equations

Balancing equations is another fundamental concept when working with linear equations. To keep an equation true, you must perform the same operation on both sides.

Consider the initial equation from our example: 1.94 = a - 2.6.
If we add 2.6 to one side, we must add the same amount to the other side to maintain the balance.
So, adding 2.6 to both sides gives us: 1.94 + 2.6 = a - 2.6 + 2.6.
It's like maintaining balance on a scale: whatever you do to one side, you have to do to the other.
This keeps the equation balanced and maintains its integrity.

This ensures that the equality is preserved throughout the process.
It's crucial for arriving at the correct solution.

simplification in algebra

Simplification in algebra involves combining like terms and simplifying expressions to make the problem easier to solve.
In our example, after balancing the equation by adding 2.6 to both sides, we are left with:
1.94 + 2.6 = a.
Next, we combine the numbers on the left side:
1.94 + 2.6 = 4.54.
This gives us the simplified equation:
4.54 = a.
Now, 'a' is isolated, and we know its value.
Simplification makes it easier to solve the equation and understand the steps we took to find the solution.

Combining like terms is a common simplification technique.
Always simplify expressions wherever possible for clarity and ease of solving.

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91影视

In the following exercises, solve. $$ 1.94=a-2.6 $$

Short Answer

Step by step solution

- Identify the Equation

- Add 2.6 to Both Sides

- Simplify the Equation

- Write the Solution

Key Concepts

isolating the variable

balancing equations

simplification in algebra

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