Problem 53 Solve each equation. \(3.2-2 b... [FREE SOLUTION]

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McGraw Hill

$Math Studyset 91影视 Explanations$ Math

2004 Edition

Chapter 6: Problem 53

Solve each equation. $3.2-2 b=1.1$

Short Answer

Expert verified

b = 1.05

Step by step solution

Isolate the variable term

Subtract 3.2 from both sides of the equation to isolate the term with the variable on one side. This gives: \[ -2b = 1.1 - 3.2 \]

Simplify the right-hand side

Calculate the right-hand side expression: \[ 1.1 - 3.2 = -2.1 \] So the equation now is: \[ -2b = -2.1 \]

Solve for the variable

Divide both sides of the equation by -2 to solve for $ b $. This gives: \[ b = \frac{-2.1}{-2} \] Simplify the expression: \[ b = 1.05 \]

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Key Concepts

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

isolating variable

To solve a linear equation, the first thing we need to do is get the variable by itself on one side of the equation. This method is called 'isolating the variable'.
In our example, we need to solve for the variable $ b $ in the equation $ 3.2 - 2b = 1.1 $.
We start by isolating the term with $ b $.
The equation can be rearranged by subtracting 3.2 from both sides: \[ 3.2 - 2b - 3.2 = 1.1 - 3.2 \]
This allows us to cancel out the constant term on the left side, making our equation: \[ -2b = 1.1 - 3.2 \]
Now we have isolated the variable term, meaning $ -2b $ is by itself on one side of the equation.

simplifying expressions

Now that we have isolated the variable term, the next step is to simplify the remaining expression.
In our equation $ -2b = 1.1 - 3.2 $, we need to perform the arithmetic on the right-hand side: \[ 1.1 - 3.2 = -2.1 \]
Therefore, the equation simplifies to: \[ -2b = -2.1 \]
Notice how we combined the constants on the right-hand side to make the calculation easier. Always ensure that you simplify expressions step-by-step to avoid mistakes and keep the equation manageable.

dividing both sides

Finally, we need to solve for the variable by getting $ b $ completely by itself.
In our simplified equation, $ -2b = -2.1 $, we will divide both sides by -2: \[\frac{-2b}{-2} = \frac{-2.1}{-2}\]
This step gives us: \[b = 1.05 \]
Dividing both sides of the equation by the coefficient of the variable is a key step in solving linear equations. It isolates the variable, allowing us to find its value. Always remember to divide both sides by the exact same number to maintain equality in the equation.

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91影视

Solve each equation. \(3.2-2 b=1.1\)

Short Answer

Step by step solution

Isolate the variable term

Simplify the right-hand side

Solve for the variable

Key Concepts

isolating variable

simplifying expressions

dividing both sides

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