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01.07.2022 - 12:27

Solve the compound inequality: 3x – 5 greater than -17 and 4x + 3 less than 15.

Question:

Solve the compound inequality: {eq}3x – 5 > -17 {/eq} and {eq}4x + 3 < 15 {/eq}.

Answers (1)

Ruth April 11, 2023 в 06:11

We can solve each inequality separately and then find the intersection of their solutions. Starting with the first inequality: $$3x - 5 > -17$$ Adding 5 to both sides: $$3x > -12$$ Dividing both sides by 3: $$x > -4$$ Now for the second inequality: $$4x + 3 < 15$$ Subtracting 3 from both sides: $$4x < 12$$ Dividing both sides by 4: $$x < 3$$ The intersection of these two solutions is any value of x that is greater than -4 and less than 3. In interval notation, this can be written as: $$-4 < x < 3$$ Or in set-builder notation: $${ x mid -4 < x < 3 }$$

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