SOLUTION: how do I solve to get the inequality when: 2x+4> 1/3

Question 566608: how do I solve to get the inequality when: 2x+4> 1/3

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
2x + 4 > 1/3
subtract 4 from both sides of the equation to get:
2x > 1/3 - 4
multiply 4 by 3/3 to get:
2x > 1/3 - 12/3
simplify to get:
2x > -11/3
divide both sides of the equation by 2 to get:
x > -11/(3*2)
simplify to get:
x > -11/6
since this can't be simplified any further, that' your answer.
confirm by substituting for x in your original equation.
pick a value of x > -11/6
pick a value for x that is greater than -11/6.
try -10/6
your original equation is:
2x + 4 > 1/3
substitute -10/6 for x to get:
2 * (-10/6) + 4 > 1/3
simplify to get:
-20/6 + 4 > 1/3
multiply 4 by 6/6 to get:
-20/6 + 24/6 > 1/3
combine like terms to get:
4/6 > 1/3
simplify to get:
2/3 > 1/3
since this equation is true, your value for x is probably good.
to make a complete test, you would need to test out when x = -11/6 and when x < -11/6.
both those tests should lead to a false equation (one that is not true).
for example:
when x = -11/6, the original equation of:
2x + 4 > 1/3 becomes:
2 * (-11/6) + 4 > 1/3
simplify to get:
-22/6 + 4 > 1/3
multiply 4 by 6/6 to get:
-22/6 + 24/6 > 1/3
combine like terms to get:
2/6 > 1/3
simplify to get:
1/3 > 1/3
this equation is false because 1/3 is equal to 1/3 and not greater than it.
the value of x = -11/6 is not valid.
this is correct because the solution to the equation said that x > -11/6, not x = to -11/6 and not x >= -11/6.

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