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Five times the difference between a number and four is greater than the quotient of four times the number and six. Find the smallest integer that will satisfy the inequality



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luana
[tex]x-\ number\\\\\ 5(x-4)>\frac{4x}{6}\ \ \ | multiply\ by\ 6\\\\ 30(x-4)>4x\\\\ 30x-120>4x\ \ \ \ | subtract\ 4x\\\\ 26x-120>0\ \ \ | add\ 120\\\\ 26x>120\ \ \ | divide\ by\ 26\\\\ x>\frac{120}{26}\\\\ x>4\frac{8}{13}[/tex]
apologiabiology
5 times (5 times) the differnce (-) a number(x) and 4(4) is greater than (>) the quotient (/) 4 times the nmber (4x) and 6 (6)

5(x-4)>4x/6
5x-20>4x/6
treat > as an equals for nnow
multiply both sides by 6
30x-120>4x
divide both sides by 2
15x-60>2x
add 60 to both sides
15x>2x+60
subtract 2x from both sides
13x>60
divide both sdie sby 13
x>60/13
the smalles tnumber is the next number bigger then 60/13

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