Question 6167
You have three questions here. Here goes ---
Sometimes it helps to rephrase the word problem in the opposite order.
7 less than 4 times a number is the same as: a number times 4, less 7.
This is {{{4x-7}}}
11 more than half a number is the same as: half a number and 11 more.
This is {{{x/2+11}}}
Can you now write 5 more than the product of a number and 3, which is the same as the product of a number and 3 and 5 more?

A reciprocal of a number is a second number such that when the two numbers are multiplied the answer is 1. The reciprocal of 7 is {{{1/7}}}. The reciprocal of {{{1/7}}} is 7. Why? Because {{{ (1)(1/7)=1}}} In fact, {{{(x)(1/x)=1}}}. So most people just say, the reciprocal of a number is 1 divided by the number. Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The general rule is reverse the numerator and the denominator and multiply. So 1 divided by a fraction is the same as 1 multiplied by the fraction "turned upside down." In general, {{{1/(x/y)=(1)(y/x)}}}
But be careful! 0 has no reciprocal! So watch out for things like {{{ 1/(0/9)}}}
There is no such thing as division by zero.
To answer your question, the first number 9/8 has the reciprocal 8/9. And so on.

Your third question asks to find t when {{{-t/12=2/3}}}
You multiply both sides by {{{-12}}} which is
{{{(-12)(-t/12)=(-12)(2/3)}}}
{{{12t/12=-24/3}}}
{{{t=-8}}}
Look closely at that first part {{{(-12)(-t/12)}}}
That's {{{(-12)(-1/12)t}}}
See the reciprocals?