# What value of x is in the solution set of 2x^{2} - 3 ≤ 7?

A solution set represents the set or range of values that a function can have for the given x values.

## Answer: The solution to this inequality is all real values of x that are in the interval [-√5, √5].

Let's go through the step-by-step solution to find the final solution.

**Explanation:**

Given expression: 2x^{2} - 3 ≤ 7

Adding 3 on both sides of the given inequality, we get

⇒ 2x^{2} - 3 + 3 ≤ 7 + 3

⇒ 2x^{2} ≤ 7 + 3

⇒ 2x^{2} ≤ 10

Dividing 2 into both sides of the above inequality, we get

⇒ 2x^{2}/2 ≤ 10/2

⇒ x^{2} ≤ 5

⇒ |x| ≤ √5

### Thus, the solution to this inequality is all real values of x lying in the interval [-√5, √5].

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