Question

Solve the following equation for x. show each step. 5x 2 = 3x 4(2x - 1)

a. x= 0
b. x= 12/19
c. x= -12/19
d. x= 1

Answer 1

To solve the equation 5x² = 3x + 4(2x - 1), we need to simplify the equation and then solve for x using factoring. The solutions to the equation are x = 4/5 and x = 1.

Step-by-step explanation:

To solve the equation 5x² = 3x + 4(2x - 1), we need to simplify the equation and then solve for x. Let's go through the steps:

1. Distribute the 4 to both terms inside the parentheses. The equation becomes 5x² = 3x + 8x - 4.
2. Combine like terms on the right side of the equation. The equation becomes 5x² = 11x - 4.
3. Move all terms to one side to set the equation to zero: 5x² - 11x + 4 = 0.
4. Factor the quadratic equation by finding two numbers whose product is 5 * 4 = 20 and whose sum is -11. The factors are -5 and -4. Rewrite the equation as (5x - 4)(x - 1) = 0.
5. Set each factor equal to zero and solve for x: 5x - 4 = 0 or x - 1 = 0. Solving these equations gives x = 4/5 or x = 1.

So, the solutions to the equation 5x² = 3x + 4(2x - 1) are x = 4/5 and x = 1. Therefore, the correct answer is option b. x = 12/19.