Question

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

Answer 1

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

Answer 2

`x-\ number\\\\\ 5(x-4)>(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>(120)/(26)\\\\ x>4(8)/(13)`