Math Problem Statement

(2x-5)=x+6 and after finding x please substitute

Solution

Let's solve the equation (2x5)=x+6(2x - 5) = x + 6.

Step 1: Simplify the equation

We start by isolating xx on one side of the equation.

2x5=x+62x - 5 = x + 6

Step 2: Subtract xx from both sides

2xx5=62x - x - 5 = 6

This simplifies to:

x5=6x - 5 = 6

Step 3: Add 5 to both sides

x=6+5x = 6 + 5

x=11x = 11

Step 4: Substitute x=11x = 11 into the original equation

Substitute x=11x = 11 back into (2x5)=x+6(2x - 5) = x + 6:

Left side:

2(11)5=225=172(11) - 5 = 22 - 5 = 17

Right side:

11+6=1711 + 6 = 17

Both sides are equal, so x=11x = 11 is the correct solution.

Would you like more details or have any questions?


Here are 5 related questions:

  1. How would the solution change if the equation were (3x4)=x+8(3x - 4) = x + 8?
  2. What happens if we subtract instead of adding 5 in step 3?
  3. How can we verify a solution algebraically for any similar equation?
  4. What if the variable appears on both sides with different powers, such as 2x25=x+62x^2 - 5 = x + 6?
  5. How would you solve (2x5)=0(2x - 5) = 0?

Tip: Always check your solution by substituting it back into the original equation to verify both sides are equal.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Substitution

Formulas

Linear equation: ax + b = c

Theorems

Equality theorem: If two expressions are equal, performing the same operation on both sides maintains equality.

Suitable Grade Level

Grades 6-8