SOLUTION: Write an inequality for each relationship. Solve each inequality Four more than twice a number is greater than two-thirds of the number

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Question 223784: Write an inequality for each relationship. Solve each inequality
Four more than twice a number is greater than two-thirds of the number
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Four more than twice a number is greater than two-thirds of the number
written as:
2x + 4 > 2%2F3x
:
Subtract 4 from both sides:
2x > 2%2F3x - 4
:
subtract 2%2F3x from both sides
2x - 2%2F3x > -4
:
which is
6%2F3x - 2%2F3x > -4
:
4%2F3x > -4
:
Multiply both sides by 3 to get rid of the denominator
4x > 3(-4)
4x > -12
:
Divide both sides by 4
x > %28-12%29%2F4
x > -3
:
:
Check solution with a value that is greater than -3, say -2
2(-2) + 4 > 2%2F3(-2)
-4 + 4 > %28-4%29%2F3
0 > -4%2F3x; that's true
:
Check solution with a value that is less than -3, say -4
2(-4) + 4 > 2%2F3(-4)
-8 + 4 > %28-8%29%2F3
-4 > -8%2F3x; that's not rue