How do you solve #5(x+4)<=4(2x+3)#?

1 Answer
Nov 5, 2015

Answer:

#x >= 8/3# by properties of inequality.

Explanation:

The first step would be to distribute each number to the parenthesis. So you would have #5x+20<=8x+12#.

Now you can subtract #5x# from each side, by the subtraction property of equality (or inequality in this case). You can subtract #8x# from each side also, but that results in a #-x# on one side and that makes it harder to work with later on. After this, you are left with #20<=3x+12#.

Now you want to isolate #x# to one side, and this can be done with the subtraction property of inequality. Subtract #12# from each side of the inequality, #8<=3x#.

The next thing you want to do is to get #x# without a coefficient. This can be done with the division property of inequality. Dividing each side by #3#, you would be left with #8/3<=x#. (By the symmetric property of inequality you can reverse the inequality sign and make it #x>=8/3#.

#8/3# can also be reduced to #2 2/3# or #2.667# (rounded to the thousandths place).