The range of values of x satisfying the inequality $$\left| 2x +3 \right|\ge7 $$ is?

Question

The range of values of x satisfying the inequality  $$\left| 2x +3 \right|\ge7 $$  is?

anonymous · Answer

@satellite73 help

saifoo.khan · Answer

Can we help too? :S

anonymous · Answer

$$2x+3\geq 7$$ or 
$$2x+3\leq -7$$ solve both inequalities for $x$ you will get two separate intervals 
saifoo claus can finish

anonymous · Answer

2x+3≥7

saifoo.khan · Answer

Haha @satellite73 .

@shameer1  there will be two different values.

anonymous · Answer

i got it as  -5  and 2   but the answer is  (-infinity,-5) U {2, infinity)

saifoo.khan · Answer

Try graphing the answers.. then you can understand this.

anonymous · Answer

hold the phone

anonymous · Answer

you are solving INEQUALITIES

anonymous · Answer

yes

anonymous · Answer

no equalities. so your solutions are intervals, not numbers. in other words when you solve 
$$2x+3\leq -7$$ subtract 3 get 
$$2x\leq -10$$ divide by 2 get 
$$x\leq 5$$ that is an inequality, means all numbers less than or equal to -5. as an interval it looks like 
$$(-\infty,-5)$$

anonymous · Answer

similarly 
$$2x+3\geq 7$$
$$2x\geq4$$
$$x\geq 2$$ all numbers greater than or equal to 2
as in interval looks like 
$$[2,\infty)$$

anonymous · Answer

actually my first interval was wrong, should have been written as 
$$(-\infty,-5]$$

anonymous · Answer

keep the inequality when you solve, do not change it to an equal sign or you will get confused at the end

anonymous · Answer

hey how that ign changes  ist equation