What is the solution set to the inequality (4x-3)(2x-1) 0

Algebra Examples

Solve for x (4x-3)(2x-1)>=0

Step 1

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .

Step 2

Set equal to and solve for .

Add to both sides of the equation.

Divide each term in by and simplify.

Cancel the common factor of .

Cancel the common factor.

Step 3

Set equal to and solve for .

Add to both sides of the equation.

Divide each term in by and simplify.

Cancel the common factor of .

Cancel the common factor.

Step 4

The final solution is all the values that make true.

Step 5

Use each root to create test intervals.

Step 6

Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.

Test a value on the interval to see if it makes the inequality true.

Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

The left side is greater than the right side , which means that the given statement is always true.

True

Test a value on the interval to see if it makes the inequality true.

Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

The left side is less than the right side , which means that the given statement is false.

False

Test a value on the interval to see if it makes the inequality true.

Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

The left side is greater than the right side , which means that the given statement is always true.

True

Compare the intervals to determine which ones satisfy the original inequality.

True

False

True

Step 7

The solution consists of all of the true intervals.

or

Step 8

The result can be shown in multiple forms.

Inequality Form:

Interval Notation:

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James W.

Algebra

8 months, 3 weeks ago

We don’t have your requested question, but here is a suggested video that might help.

Related Question

Solve the inequality 3 − |2 − 4x| ≤ −2

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Video Transcript

Someone just track three on both sides. That's what gives me negative. Mm hmm. Negative five. All right. So when I divide or multiply both sides. Times negative one. That makes me flip my sign. So the absolute value to minus four X. Gonna flip. That sign is greater than equal to five. Alright, So then that gives me two minus four X. Is greater than or equal to five and two minus four X is greater or less than Or equal to negative five. So, I'm going to subtract two on both sides. These so negative four X. Is less than or equal to negative seven, divided by negative four on both sides. So X. Is greater than or equal to Because again, I gotta put that sign. 7/4 Over here. Subtract two on both sides. It's a negative four X. Is greater than or equal to three, Divide by -4, divide by -4. Again, I've gotta flip that sign. So that's negative 3/4. So those are your answers.

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Daniel M.

Algebra

3 months, 3 weeks ago

We don’t have your requested question, but here is a suggested video that might help.

Related Question

Solve each equation or inequality. $$ \left|\frac{x-4}{3 x+1}\right| \geq 0 $$

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Video Transcript

Okay, so you know that ah for first we need to find the domain of this uh inequality. Okay, so the domain is X. X. Does not, he goes to -1 over ST Or you can write that minus infinity minus one. Worth three. You need one is 1/3 infinity. Okay? So uh we know that the absolute value of any real number must be greater equals zero. So to solve this inequality we know that this is in natural stance. Okay. For animal number it's always stand. Okay? So and the solution, it's just our domain. Okay, So the solution set is minus infinity minus 1/3, unit minus 1/3 infinity. Okay?