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Solve the following equation.
(x - 1)(4x + 3) = 0
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A . The solution set is _______
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B . There is no solution.

Sagot :

wegnerkolmp2741o

Answer:

The solution set is 1, -3/4

Step-by-step explanation:

(x - 1)(4x + 3) = 0

We can use the zero product property to solve for x

x-1 =0  4x+3 =0

x=1          4x=-3

                 x = -3/4

The solution set is 1, -3/4

The solutions to the equation (x - 1)(4x + 3) = 0 are x = 1 and x = -3/4.

To solve this, we need to understand that if the product of two factors is zero, then at least one of the factors must be zero. So, we set each factor equal to zero and solve for x:

  1. x - 1 = 0
    Adding 1 to both sides gives us:
    x = 1
  2. 4x + 3 = 0
    Subtracting 3 from both sides gives us:
    4x = -3
    Dividing both sides by 4 gives us:
    x = -3/4

Thus, the solutions are x = 1 and x = -3/4. Therefore, the solution set is 1, -3/4.

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