Question

What is the solution set to the inequality (4x-3)(2x-1)20?

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Answer 1

The given question is wrong.

Question:

What is the solution set to the inequality (4x – 3) (2x – 1) ≥ 0?

(A)
`\{x| x\leq 3\ \text {or} \ x\geq 1`

(B)
`\{x| x\leq 2\ \text {or} \ x\geq (4)/(3)`

(C)
`\{x| x\leq (1)/(2)\ \text {or} \ x\geq (3)/(4)`

(D)
`\{x| x\leq (-1)/(2)\ \text {or} \ x\geq (-3)/(4)`

Answer:

The solution set to the given inequality is
`\{x| x\leq (1)/(2)\ \text {or} \ x\geq (3)/(4)`.

Solution:

Given expression is (4x – 3) (2x – 1) ≥ 0.

Let us take the expression is equal to zero.

(4x – 3) (2x – 1) = 0

By quadratic factor, If AB = 0, then A = 0 or B = 0.

(4x – 3) = 0 or (2x – 1) = 0

Let us take the first factor equal to zero.

⇒ 4x – 3 = 0

⇒ 4x = 3

`$x=(3)/(4)`

Now, take the second factor equal to zero.

⇒ 2x – 1 = 0

⇒ 2x = 1

`$x=(1)/(2)`

So,
`$x=(1)/(2),x=(3)/(4)`.

Now, write it in the inequality to make the statement true.

`$x\geq (1)/(2)\ \text{(or)}\ x\leq (3)/(4)`

Option C is the correct answer.

The solution set to the given inequality is
`\{x| x\leq (1)/(2)\ \text {or} \ x\geq (3)/(4)`.