Find all value of x where 5 - x^2 < 8

• zeion
In summary, the solution set for the inequality 5 - x^2 < 8 is all real numbers, as x2 is always greater than any negative number and therefore x can be any real number.
zeion

Homework Statement

Find all value of x where 5 - x^2 < 8

The Attempt at a Solution

$$-x^2 < 3 \Rightarrow x^2 > -3 \Rightarrow x > \sqrt{-3}$$

But I can't square root a negative number?

zeion said:

Homework Statement

Find all value of x where 5 - x^2 < 8

The Attempt at a Solution

$$-x^2 < 3 \Rightarrow x^2 > -3 \Rightarrow x > \sqrt{-3}$$

But I can't square root a negative number?
x2 > -3 for all real numbers.

Mark44 said:
x2 > -3 for all real numbers.

So does that mean x is the set of all real numbers? Because any real number squared is positive.

Yes, the solution set is all real numbers. Something to remember: If you ever get an equation where x2 > some negative number, the inequality is true for all real numbers.

1. What is the equation being solved in this problem?

The equation being solved is 5 - x^2 < 8.

2. What does the inequality symbol (<) mean in this equation?

The inequality symbol means "less than" in this equation.

3. How do you solve an inequality like this one?

To solve this inequality, we need to isolate the variable x on one side of the inequality symbol and all other terms on the other side. Then, we can use algebraic operations to find the range of values for x that satisfy the inequality.

4. What are the possible values of x that satisfy this inequality?

The possible values of x that satisfy this inequality are all real numbers that are less than the square root of 3 or greater than negative square root of 3.

5. Is there a specific method or strategy to solve this type of inequality?

Yes, there are specific methods and strategies to solve this type of inequality. One method is to graph the inequality on a number line and identify the solutions visually. Another method is to use algebraic operations to isolate the variable and solve for its range of values. There are also rules for solving inequalities involving exponents and logarithms.

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