Question

PLS HELP any hints appericated(40 Points)

A few algebra problems,
1.Solve the equation: [4ax - (a + b)](a + b) = 0, where a and b are constants.
2.Solve the equation m^2x + 1 = m(x + 1), where m is a parameter.
3.Given that the equation a(2x - 1) = 3x - 3 has no solution, find the value of the parameter a.

Answer 1

• See below

Explanation:

1) Solve the equation: [4ax - (a + b)](a + b) = 0, where a and b are constants.

• if a + b = 0, then x has infinitely many solutions

or

• 4ax = a + b
• x = (a + b)/4a, a≠0

2) Solve the equation m²x + 1 = m(x + 1), where m is a parameter.

• m²x + 1 - mx - m = 0
• (m²- m)x = m - 1
• m(m - 1)x = m - 1
• mx = 1
• x = 1/m, m≠0

3) Given that the equation a(2x - 1) = 3x - 3 has no solution, find the value of the parameter a.

• a(2x - 1) = 3x - 3
• 2ax - a = 3x - 3
• 2ax - 3x = a - 3
• (2a - 3)x = a - 3
• x = (a - 3)/(2a - 3)

The equation has no solution if:

• 2a - 3 = 0
• 2a = 3
• a = 1.5