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Chapter 8: Problem 7

In the following exercises, solve each equation. $$ b+\frac{1}{4}=\frac{3}{4} $$

Short Answer

Expert verified
The value of \( b \) is \( \frac{1}{2} \).

Step by step solution

01

Understand the Equation

The given equation is: \[ b + \frac{1}{4} = \frac{3}{4} \]We need to solve for the variable \( b \).
02

Isolate the Variable

Subtract \( \frac{1}{4} \) from both sides of the equation to isolate \( b \):\[ b + \frac{1}{4} - \frac{1}{4} = \frac{3}{4} - \frac{1}{4} \]
03

Simplify Both Sides

Simplify the equation:\[ b = \frac{3}{4} - \frac{1}{4} \]Subtract the fractions:\[ b = \frac{2}{4} \]
04

Simplify the Fraction

Reduce \( \frac{2}{4} \) to its simplest form:\[ b = \frac{1}{2} \]

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Key Concepts

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

isolate the variable
In any equation, the goal is often to find the value of the unknown variable. To do this, we need to isolate the variable on one side of the equation.

The initial equation we have is:








  • To isolate the variable:
      To find out, we subtract

      • Hence, we have:

        • 路

        • 路
          We then simplify to:
        • Now that is isolated, we move on to the next step.
subtracting fractions
Subtracting fractions can seem tricky at first, but it鈥檚 quite manageable. Here, we need to subtract Let us break down the steps:

    • Here's how you do it:
        We then get:
            • Now, we have:
              Learning to subtract fractions is a helpful skill for solving many types of equations.
simplifying fractions
Simplifying fractions means reducing them to their lowest terms. This makes them easier to understand and work with.

Consider the fraction we ended up with: To simplify :
  • Find the
  • 路
  • Divide the
    We have: So, the solution is simplified to: Simplifying fractions ensures we present answers in the clearest form.

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