Sure, let's solve each equation step-by-step using the balancing method.
### Equation (a): [tex]\( 11 + 2q = 19 \)[/tex]
1. Isolate the term with [tex]\( q \)[/tex]:
- Subtract 11 from both sides:
[tex]\[ 11 + 2q - 11 = 19 - 11 \][/tex]
- Simplify the equation:
[tex]\[ 2q = 8 \][/tex]
2. Solve for [tex]\( q \)[/tex]:
- Divide both sides by 2:
[tex]\[ \frac{2q}{2} = \frac{8}{2} \][/tex]
- This simplifies to:
[tex]\[ q = 4 \][/tex]
So, the solution for the first equation is:
[tex]\[ q = 4 \][/tex]
### Equation (b): [tex]\( \frac{3a}{5} = 15 \)[/tex]
1. Eliminate the denominator:
- Multiply both sides by 5 to clear the fraction:
[tex]\[ 5 \times \frac{3a}{5} = 15 \times 5 \][/tex]
- Simplify the equation:
[tex]\[ 3a = 75 \][/tex]
2. Solve for [tex]\( a \)[/tex]:
- Divide both sides by 3:
[tex]\[ \frac{3a}{3} = \frac{75}{3} \][/tex]
- This simplifies to:
[tex]\[ a = 25 \][/tex]
So, the solution for the second equation is:
[tex]\[ a = 25 \][/tex]
In summary, the solutions to the equations are:
[tex]\[ q = 4 \][/tex]
[tex]\[ a = 25 \][/tex]
