Solve the equation. Use set notation to express the solution set of the equation has no solution or if the equation is true for all real numbers.

Question

X/4-x/12+8=x+8

Answer 1

To solve the equation, let's simplify each side:

X/4 - x/12 + 8 = x + 8
Multiply every term by 12 to eliminate fractions:

3x - x + 96 = 12x + 96
Combine like terms:

2x + 96 = 12x + 96
Subtract 2x from both sides:

96 = 10x + 96
Subtract 96 from both sides:

0 = 10x
Divide every term by 10:

0 = x

The equation simplifies to x = 0.

Since this equation has a distinct solution, the solution set is {0}.