Math Problem Statement

consider the equation x/a + b = c. solve the equation for b in terms of a,c and x.

Solution

To solve the equation xa+b=c\frac{x}{a} + b = c for bb, follow these steps:

Given equation:

xa+b=c\frac{x}{a} + b = c

Step 1: Isolate bb

Subtract xa\frac{x}{a} from both sides of the equation: b=cxab = c - \frac{x}{a}

Final answer:

b=cxab = c - \frac{x}{a}

Would you like any additional details or have further questions?

Here are 5 related questions to extend the topic:

  1. How would you solve the equation 2xa+b=c\frac{2x}{a} + b = c for bb?
  2. What happens if a=0a = 0 in the equation xa+b=c\frac{x}{a} + b = c?
  3. If c=5c = 5, a=2a = 2, and x=6x = 6, what is the value of bb?
  4. How can we express aa in terms of bb, cc, and xx in the equation xa+b=c\frac{x}{a} + b = c?
  5. How does the solution change if the equation were axb+c=d\frac{ax}{b} + c = d?

Tip: Always perform operations step by step when solving for a variable to avoid mistakes and make the process clearer.

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Math Problem Analysis

Mathematical Concepts

Algebra
Equation Solving
Variables

Formulas

b = c - x/a

Theorems

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Suitable Grade Level

Grades 6-8