# How do you solve the inequality #abs(3-x)<=3#?

##### 2 Answers

#### Explanation:

#"Given the inequality " |x|<=a#

#"the solution is always of the form " -a<=x<=a#

#rArr-3<=color(red)(3-x)<=3# Isolate x in the centre interval while obtaining numeric values in the 2 end intervals.

subtract 3 from ALL intervals.

#-3-3<=cancel(3)cancel(-3)-x<=3-3#

#rArr-6<=-x<=0# multiply by - 1 to obtain x

#color(blue)"Note"# when multiplying/dividing an inequality by a#color(blue)"negative"# value we must#color(red)" reverse the inequality symbol"#

#rArr6>=x>=0larrcolor(red)" reverse symbol"#

#rArrx<=6color(red)" and " x>=0#

#rArr0<=x<=6" is the solution"#

#x in [0,6]larrcolor(red)" in interval notation"#

#### Explanation:

We can rewrite the equation as

Other notations for this answer: