Question 223784
Four more than twice a number is greater than two-thirds of the number
written as:
2x + 4 > {{{2/3}}}x
:
Subtract 4 from both sides:
2x > {{{2/3}}}x - 4
:
subtract {{{2/3}}}x from both sides
2x - {{{2/3}}}x > -4
:
which is
{{{6/3}}}x - {{{2/3}}}x > -4
:
{{{4/3}}}x > -4
:
Multiply both sides by 3 to get rid of the denominator
4x > 3(-4)
4x > -12
:
Divide both sides by 4
x > {{{(-12)/4}}}
x > -3
:
:
Check solution with a value that is greater than -3, say -2
2(-2) + 4 > {{{2/3}}}(-2)
-4 + 4 > {{{(-4)/3}}}
0 > {{{-4/3}}}x; that's true
:
Check solution with a value that is less than -3, say -4
2(-4) + 4 > {{{2/3}}}(-4)
-8 + 4 > {{{(-8)/3}}}
-4 > {{{-8/3}}}x; that's not rue