How do you solve #\frac { 3} { 2} - \frac { 2} { 9} x > - \frac { 1} { 8} ( x - 19)#?

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Answer 1 · 2018-01-06T11:52:40

#x < -9 #

This is an inequalities question, but we can treat it like ussual algebra:

First expanding the right side:

#3/2 - 2/9 x > -1/8x + 19/8 #

Subtracting #3/2# form both sides:

#-2/9x > -1/8 x + 19/8 - 3/2 #

Plussing #1/8x# on both dies:

#-2/9x + 1/8x > 19/8 - 3/2 #

Finding common denominators for each side individully:

# (-2*8 )/ (9*8) x + (1*9) / (8*9) x > 19/8 - (3*4)/(2*4) #

# (-16 + 9 )/(72) x > (19-12 )/8 #

#-7/72 x > 7/8 #

Multiply by 72:

#-7x > 63 #

Dividing by #7# :

#-x > 9 #

Multiply by #-1#

#color(red)(x < -9 #

Not forgetting when we divide or multiply by a negative, the ineqaulity flips!