Solve the equation 4(x - 1) - x = 3(x + 5) - 11.

Solution:

Let us solve the equation by transposing method and isolating the variable x.

Step 1: Solve the bracket, using the distributive property.

⇒ 4x - 4 - x = 3x + 15 - 11

Step 2: Transpose the terms and isolate the variable.

4x - 4 - x = 3x + 15 - 11

= 4x - 3x - x = 4 + 15 - 11

Add/subtract the like terms.

⇒ 0x = 4

Step 3: Finally, we get no solution.

Thus, the equation 4x - 4 - x = 3x + 15 - 11 has no value of x which satisfies the equation.

Solve the equation 4(x - 1) - x = 3(x + 5) - 11.

Summary:

The system of equations 4x - 4 - x = 3x + 15 - 11 has no solution for x and therefore x ∈ ∅.