Math Problem Statement

(2x-7)-(x-5)=0

Solution

To solve the equation:

(2x7)(x5)=0(2x - 7) - (x - 5) = 0

Step 1: Simplify the equation.

First, distribute the negative sign through the second parentheses:

2x7x+5=02x - 7 - x + 5 = 0

Step 2: Combine like terms.

Now, combine the terms involving xx and the constants:

(2xx)+(7+5)=0(2x - x) + (-7 + 5) = 0

This simplifies to:

x2=0x - 2 = 0

Step 3: Solve for xx.

To isolate xx, add 2 to both sides:

x=2x = 2

Thus, the solution is:

x=2x = 2

Would you like further details or explanations on any step?

Related Questions:

  1. What happens if we had a coefficient in front of both expressions?
  2. How do you solve similar equations with variables on both sides?
  3. What if there were multiple terms with xx in parentheses?
  4. Can this be solved graphically by plotting both sides of the equation?
  5. How do we handle equations with fractions?

Tip: Always simplify expressions inside parentheses and distribute negatives carefully to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Simplification

Formulas

Basic linear equation structure: ax + b = 0

Theorems

Distributive Property
Properties of Equality

Suitable Grade Level

Grades 6-8