Question 529979
I believe they mean that after figuring out three fourth the number, then you increase that by 32. That would be, following tradition by calling the mistery number {{{x}}},
{{{(3/4)*x+32}}}
If it's no more than 58, then it's less than or equal to 58, so
{{{(3/4)*x+32<=58}}}
You do the same operations to both sides, carefully undoing what has been done to {{{x}}}.
First we subtract 32 (undoing the last thing done) to get
{{{(3/4)*x<=58-32}}} or {{{(3/4)*x<=26}}}
Then we undo the three fourths calculation/multiplication by dividing by{{{3/4}}}, which means mutiplying by {{{4/3}}}
to get
{{{x<=26*(4/3)}}} or {{{x<=104/3}}} or {{{x<=34+(2/3)}}}
CAUTION:
When multiplying/dividing both sides of an inequality by the same number, you have to be careful. If the number is negative, you have to flip < to > and viceversa. For example, it should be obvious that if
{{{x<0}}} then multiplying both sides by {{{-1}}}
it makes sense to get {{{-x>0}}}.