How do you graph the solution of #2/3(12-x)>4# on a number line?

1 Answer
Jim G.
Mar 13, 2017

#x<6#

Explanation:

The first step is to distribute the bracket.

#rArr8-2/3x>4#

subtract 8 from both sides.

#cancel(8)cancel(-8)-2/3x>4-8#

#rArr-2/3x> -4#

To make the x term positive, multiply both sides by - 1

#color(blue)"NOTE"# when multiplying/dividing an inequality by a negative quantity the inequality symbol must be #color(red)"reversed"#

#(-1)xx-2/3x< (-1)xx(-4)larrcolor(red)" reverse symbol"#

#rArr2/3x<4#

To solve for x multiply both sides by #3/2#

#(3/2xx2/3x)<(3/2xx4)#

#rArrx<6#

To show the solution on a number line, #color(blue)"place an open circle "@# at 6. This indicates that x is not equal to 6. If x was equal to 6 we would place a #color(blue) " solid circle " # • at 6. Draw an #color(blue)"arrowed line "# to the left of 6 indicating the direction of the solution

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