Certainly! Let's solve the inequality step-by-step.
Step 1: Write down the initial inequality
[tex]\[ 50q + 43 > -11q + 70 \][/tex]
Step 2: Collect all [tex]\( q \)[/tex]-terms on one side of the inequality
To do this, add [tex]\( 11q \)[/tex] to both sides:
[tex]\[ 50q + 11q + 43 > 70 \][/tex]
[tex]\[ 61q + 43 > 70 \][/tex]
Step 3: Isolate the [tex]\( q \)[/tex]-term
Subtract 43 from both sides:
[tex]\[ 61q + 43 - 43 > 70 - 43 \][/tex]
[tex]\[ 61q > 27 \][/tex]
Step 4: Solve for [tex]\( q \)[/tex]
Divide both sides by 61:
[tex]\[ q > \frac{27}{61} \][/tex]
Step 5: Simplify the fraction to its lowest terms
In this case, [tex]\(\frac{27}{61}\)[/tex] is already in its simplest form because 27 and 61 do not have any common factors other than 1.
So, the solution to the inequality is:
[tex]\[ q > \frac{27}{61} \][/tex]
This is the lowest terms and simplest form of the fraction. Thus, we have:
[tex]\[ q > \frac{27}{61} \][/tex]
