1. ## find solution

find the step by step solution

2. Originally Posted by ea12345
find the step by step solution

$|2x-7|>3$

Solve this absolute value inequality using the following model:

If $|a|>b$, then $a<-b \ \ or \ \ a>b$

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$-5\leq\frac{4-3x}{2}<1$

Multiply through by 2

$-10\leq4-3x<2$

Subtract 4 throughout the inequality

$-14\leq-3x<-2$

Divide by -3 (don't forget to reverse the inequality signs here)

Can you finish?

3. ## Thanks

4. Originally Posted by Angel
|2x-7|>3
2x-7>+-3 (When we remove the module sign, we put +- both sign for other side)

so,
-3<2x-7<3 (Take both -3 and +3, -ve will be less than 2x-7 and +ve will be greater than 2x-7)

-3<2x-7 , 2x-7<3 (Take saperate -ve and +ve and solve)
4<2x , 2x<10
2<x , x<5
x>2

2<x<5 required solution (write both answers combinely)
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Thanks,
Angel
I must make a correction in your post, Angel. This absolute value inequality is not a conjunction, rather it is a disjunction. Knowing that, we use the following model:

$\boxed{If \ \ |a|>b, \ \ then \ \ a<-b \ \ or \ \ a>b}$

$|2x-7|>3$ means:

$2x-7<-3 \ \ or \ \ 2x-7>3$

$2x<4 \ \ or \ \ 2x>10$

$x<4 \ \ or \ \ x>5$

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