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Chapter 1: Problem 15

Mentally solve each equation. $$ 2 x-3=0 $$

Short Answer

Expert verified
The solution is \(x = 1.5\)

Step by step solution

01

- Isolate the variable term

To isolate the variable term, add 3 to both sides of the equation:\[2x - 3 + 3 = 0 + 3\]This simplifies to:\[2x = 3\]
02

- Solve for the variable

Divide both sides of the equation by 2 to solve for \(x\):\[\frac{2x}{2} = \frac{3}{2}\]This simplifies to:\[x = \frac{3}{2}\]or equivalently,\[x = 1.5\]

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Key Concepts

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

Isolating the Variable
When solving linear equations, a common goal is isolating the variable. This means we want to get the variable alone on one side of the equation. Consider our example equation:

\[2x - 3 = 0\]

To isolate the term containing the variable (\
Addition Property of Equality
The addition property of equality states that if you add the same number to both sides of an equation, the equality is still true. In our example:

\[2x - 3 = 0\]

To get closer to isolating the variable term (\
Division Property of Equality
The division property of equality means that dividing both sides of an equation by the same non-zero number keeps the equality true. For our simplified equation:

\[2x = 3\]

We divide both sides by 2:

\[\frac{2x}{2} = \frac{3}{2}\]

This results in
\[x = \frac{3}{2}\]

Or as a decimal,
x = 1.5.

This step is crucial because it completes the process of solving for the variable.

Remember, you can always check your work by substituting
the variable back into the original equation to see if the equality holds.

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