Question

-3|2x+1|<4 how is this solved

Answer 1

True for all x

Explanation:

• Multiply by -1. This reverses the inequality.

`-3\left|2x+1\right| < 4\\\left(-3\left|2x+1\right|\right)\left(-1\right) > 4\left(-1\right)`

• Remember: Negative * Positive = Negative
• Remember: Negative * Negative = Positive

`3\left|2x+1\right| > -4:\:Solve\\4* -1 = -4\\\left(-3|2x+1|\right)\left(-1\right)\\\left(-3* -1\right)\\\left(-3|2x+1|)`

• Divide by 3

`=(3\left|2x+1\right|)/(3) > (-4)/(3)`

___________

`(3\left|2x+1\right|)/(3)\\(3)/(3)\\= (1)/(1)`

___________

`= (1)/(1) > (-4)/(3)`

___________

`-(4)/(3)\\= -(4)/(3)`

• Because absolute values are greater than or equal to 0, the problem will be classified as "True" for any value of x no matter what.

Hope this helps.