Question Video: Solving Compound Inequalities | Nagwa Question Video: Solving Compound Inequalities | Nagwa

Question Video: Solving Compound Inequalities Mathematics

Find all the values of π₯ that satisfy the compound inequality 7π₯ β 5 > β12 or 6π₯ + 3 β₯ 15.

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Video Transcript

Find all the values of π₯ that satisfy the compound inequality seven π₯ minus five is greater than negative 12 or six π₯ plus three is greater than or equal to 15.

We will begin by solving each of the inequalities in turn. Firstly, we have seven π₯ minus five is greater than negative 12. Adding five to both sides gives us seven π₯ is greater than negative seven as negative 12 plus five equals negative seven. We can then divide both sides of this inequality by seven such that π₯ is greater than negative one.

The second inequality states that six π₯ plus three is greater than or equal to 15. We begin by subtracting three from both sides so that six π₯ is greater than or equal to 12. We can then divide both sides of this inequality by six giving us π₯ is greater than or equal to two.

The keyword in the question here is βor.β We donβt need both of the inequalities to be true, just one of them. We can represent the first inequality on a number line as shown. We have an open circle at negative one, and π₯ can take any value greater than this. The second solution, π₯ is greater than or equal to two, can be represented by a solid circle at the value two. π₯ can take any value equal to or greater than this.

If π₯ is greater than or equal to two, it is also greater than negative one. This means that the values of π₯ that satisfy the compound inequality seven π₯ minus five is greater than negative 12 or six π₯ plus three is greater than or equal to 15 is π₯ is greater than negative one.

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