Question

Match each equation to its factorized version and solution. 24x – 6x2 = 0 2x(x 3) = 0 solution: x = 0, x = -3 14x – 7x2 = 0 6x(4 – x) = 0 solution: x = 0, x = 4 2x2 6x = 0 x(4 – x) = 0 solution: x = 0, x = 4 4x – x2 = 0 7x(2 – x) = 0 solution: x = 0, x = 2

Answer 1

To factorize and solve the given equations, we rearrange them into quadratic equations that equal 0. We then use methods like factoring or the quadratic formula to find the solutions. The step-by-step solution is provided for each equation.

Step-by-step explanation:

To factorize and solve the given equations, we need to rearrange them into quadratic equations that equal 0. Then, we can use different methods, such as factoring or the quadratic formula, to find the solutions for each equation. Let's go through the steps for each equation:

Equation 1:

24x – 6x² = 0

Rearranging it into a quadratic equation: -6x² + 24x = 0

Factoring out a common factor of -6x: -6x(x - 4) = 0

Solution: x = 0, x = 4

Equation 2:

14x – 7x² = 0

Rearranging it into a quadratic equation: -7x² + 14x = 0

Factoring out a common factor of -7x: -7x(x - 2) = 0

Solution: x = 0, x = 2

Equation 3:

2x² - 6x = 0

Rearranging it into a quadratic equation: 2x² - 6x = 0

Factoring out a common factor of 2x: 2x(x - 3) = 0

Solution: x = 0, x = 3

Equation 4:

4x – x² = 0

Rearranging it into a quadratic equation: -x² + 4x = 0

Factoring out a common factor of -x: -x(4 - x) = 0

Solution: x = 0, x = 4