Question

The equation 5x - (3x + 8) = m(4x -8 ) has no solution. What is the value of m ?

Answer 1

The value of m that makes the equation 5x - (3x + 8) = m(4x -8 ) have no solution is m = 0.5.

Step-by-step explanation:

The equation 5x - (3x + 8) = m(4x -8 ) can be simplified as follows:

1. Distribute the negative sign in -(3x + 8) to both terms inside the parentheses: -3x - 8
2. Combine like terms on the left side of the equation: 5x - 3x - 8 = m(4x -8 )
3. Combine like terms on the right side of the equation: 2x - 8 = m(4x - 8)
4. Distribute the m to both terms inside the parentheses: 2x - 8 = 4mx - 8m
5. Rewrite the equation in standard form: 2x - 4mx = 8 - 8m
6. Combine like terms on the left side of the equation: (2 - 4m)x = 8 - 8m
7. The equation has no solution when the coefficient of x on the left side of the equation is zero: 2 - 4m = 0
8. Solve for m: 4m = 2 => m = 0.5

Therefore, the value of m that makes the equation 5x - (3x + 8) = m(4x -8 ) have no solution is m = 0.5.