The solution set to this inequality is x < 14 ⇒ x ∈ (-∞, 14).
The graph for the solution set is attached.
What is an inequality?
- In mathematics, inequality describes the relationship between two algebraic expression or between two numbers. Like, greater than(>), less than(<), less than or equal to(≤), greater than or equal to(≥).
- Inequality can be treated similar to the equations and can be solved using the same mathematical techniques.
Given: Inequality
-2(x + 6) > -40
Now, we have to solve this inequality for x.
⇒ -2(x + 6) > -40
⇒ -2x - 12 > -40
Now, on adding +40 on both the the sides of the inequality, we get:
⇒ -2x - 12 + 40 > -40 + 40
⇒ -2x + 28 > 0
Now, on adding -28 on both the the sides of the inequality, we get:
⇒ -2x + 28 - 28 > -28
⇒ -2x > -28
Now, on multiplying both the sides of the inequality by -1, we get:
⇒ 2x < 28
Dividing both the sides of the inequality by 2, we get:
⇒ x < 14
⇒ x ∈ (-∞, 14)
According to this inequality, 14 will not be included in the domain.
Therefore, for the given inequality the solution set is x ∈ (-∞, 14) and the graph for the set is attached.
Learn more about the Inequality here: https://brainly.com/question/26837070?referrer=searchResults
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