Does anyone know how to solve |4x+3|-9<5

Mathematics

1 answer:

elixir [45]2 years ago

6 0

Answer in fraction form: -17/4 < x < 11/4

Answer in decimal form: -4.25 < x < 2.75

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Work Shown:

|4x+3| - 9 < 5

|4x+3| < 5+9 .... adding 9 to both sides

|4x+3| < 14

-14 < 4x+3 < 14 .... see note at the bottom

-14-3 < 4x < 14-3 .... subtracting 3 from all sides

-17 < 4x < 11

-17/4 < x < 11/4 .... divide all sides by 4

-4.25 < x < 2.75

This says that x is between -4.25 and 2.75, but x is not equal to either endpoint.

Note: I used the rule that |x| < k becomes -k < x < k where k is a positive real number.

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What is the solution of x=2+ square root x-2?

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So I'm going to assume that this question is asking for non extraneous solutions, or solutions that are found in the equation and are valid solutions when plugged back into the equation. So firstly, subtract 2 on both sides of the equation:

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Now we are going to be factoring by grouping to find the solution(s). Firstly, what two terms have a product of 6x^2 and a sum of -5x? That would be -3x and -2x. Replace -5x with -2x - 3x:

$x^2-2x-3x+6=0$