Is x^2 + x < 0 Solvable?

Thread starter adelin
Start date Jul 4, 2013
Tags

Inequality

In summary, to represent an inequality on a number line, identify the variable and inequality sign, plot a point, and draw an arrow in the direction of the inequality. Solving an equation and solving an inequality have similar processes, but the goal is different. To check the correctness of an inequality solution, substitute the value of the variable into the original inequality. You can switch the inequality sign when solving an inequality, but you must also switch the direction. Common mistakes to avoid when solving inequalities include not simplifying both sides, forgetting to switch the direction when dividing by a negative number, and confusing the order of operations. It is important to check your work to avoid these mistakes.

Jul 4, 2013

adelin

Homework Statement

x^2+x<0

[

Physics news on Phys.org

Jul 4, 2013

Curious3141

Homework Helper

adelin said:

Homework Statement

x^2+x<0

[

What do you think you should try first?

You have to show effort.

Jul 4, 2013

adelin

Curious3141 said:

What do you think you should try first?

You have to show effort.

Thanks any way.
I have found the answer.

1. How do I represent an inequality on a number line?

To represent an inequality on a number line, first identify the variable and the inequality sign. Then, plot a point on the number line at the value of the variable. If the inequality is inclusive (≤ or ≥), use a closed circle on the point. If the inequality is exclusive (< or >), use an open circle. Finally, draw an arrow in the direction of the inequality.

2. What is the difference between solving an equation and solving an inequality?

The process of solving an equation and solving an inequality is similar, but there is one key difference. When solving an equation, the goal is to find the value(s) of the variable that make the equation true. When solving an inequality, the goal is to find the range of values for the variable that make the inequality true.

3. How do I know if my solution to an inequality is correct?

To check if your solution to an inequality is correct, you can substitute the value of the variable into the original inequality and see if it makes a true statement. If it does, then your solution is correct. If it does not, then your solution is incorrect.

4. Can I switch the inequality sign when solving an inequality?

Yes, you can switch the inequality sign when solving an inequality, but you must also switch the direction of the inequality. For example, if you have 5x > 10, you can divide both sides by 5 to get x > 2. However, if you divide by a negative number, you must also switch the direction of the inequality. For example, if you have -3x < 9, you can divide both sides by -3 to get x > -3.

5. What are some common mistakes to avoid when solving inequalities?

Some common mistakes to avoid when solving inequalities include forgetting to switch the direction of the inequality when dividing by a negative number, not simplifying both sides of the inequality before solving, and confusing the order of operations. It is important to be careful and check your work when solving inequalities to avoid these mistakes.