Final answer:
To solve the equation ( 13x + 2 ) ( 5x – 7 ) ( 3x – 4 ), we find where the expression equals zero by setting each factor to zero individually, resulting in the solutions x = -2/13, x = 7/5, and x = 4/3.
Step-by-step explanation:
To solve the equation (13x + 2)(5x – 7)(3x – 4), we must find the values of x that make the expression equal to zero. This is a product of three factors, and a product equals zero only when at least one of the factors is zero. Therefore, we can set each factor equal to zero and solve for x separately.
- 13x + 2 = 0 → x = -2/13
- 5x – 7 = 0 → x = 7/5
- 3x – 4 = 0 → x = 4/3
Thus, the equation has three real solutions for x: -2/13, 7/5, and 4/3. It is often a good practice to check the answer to see if it is reasonable by substituting the values of x back into the original equation.