find the step by step solution
Thanks in advance
$\displaystyle |2x-7|>3$
Solve this absolute value inequality using the following model:
If $\displaystyle |a|>b$, then $\displaystyle a<-b \ \ or \ \ a>b$
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$\displaystyle -5\leq\frac{4-3x}{2}<1$
Multiply through by 2
$\displaystyle -10\leq4-3x<2$
Subtract 4 throughout the inequality
$\displaystyle -14\leq-3x<-2$
Divide by -3 (don't forget to reverse the inequality signs here)
Can you finish?
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:
$\displaystyle \boxed{If \ \ |a|>b, \ \ then \ \ a<-b \ \ or \ \ a>b}$
$\displaystyle |2x-7|>3$ means:
$\displaystyle 2x-7<-3 \ \ or \ \ 2x-7>3$
$\displaystyle 2x<4 \ \ or \ \ 2x>10$
$\displaystyle x<4 \ \ or \ \ x>5$
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