How do you solve the inequality #7x – 2<3(3x + 2) #?

1 Answer
May 14, 2018

Answer:

#x > 4#

Explanation:

#7x - 2 < 3(3x+2)#

First, use the distributive property to simplify #color(blue)(3(3x+2))#:

#color(blue)(3(3x+2) = (3 * 3x) + (3 * 2) = 9x + 6)#

Now put that back into the inequality:
#7x - 2 < 9x + 6#

Subtract #color(blue)6# from both sides of the inequality:
#7x - 2 quadcolor(blue)(-quad6) < 9x + 6 quadcolor(blue)(-quad6)#

#7x - 8 < 9x#

Subtract #color(blue)(7x)# from both sides of the inequality:
#7x - 8 quadcolor(blue)(-quad7x) < 9x quadcolor(blue)(-quad7x)#

#-8 < 2x#

Divide both sides by #color(blue)2#:
#-8/color(blue)(2) < (2x)/color(blue)2#

#4 < x#

This can be read as "4 is less than x".

Since we want the variable on the left side, it becomes "x is more than 4, or:

#x > 4#

Hope this helps!