It looks like you've uploaded a math worksheet. Let me transcribe and solve the two problems visible in the image.

1. First problem: $19 - \frac{x}{2} = 11 - \frac{7}{2}$

2. Second problem: $18x - 9 - 10x = 63$

Problem 1:

$19 - \frac{x}{2} = 11 - \frac{7}{2}$

Step 1: Simplify the constants $19 = \frac{38}{2}, \quad 11 = \frac{22}{2}$ $19 - \frac{x}{2} = \frac{38}{2} - \frac{x}{2}, \quad 11 - \frac{7}{2} = \frac{22}{2} - \frac{7}{2} = \frac{15}{2}$ Thus, the equation becomes: $\frac{38}{2} - \frac{x}{2} = \frac{15}{2}$

Step 2: Combine like terms $\frac{38 - x}{2} = \frac{15}{2}$

Step 3: Clear the denominator by multiplying by 2 $38 - x = 15$

Step 4: Solve for $x$ $x = 38 - 15 = 23$ So, $x = 23$.

Problem 2:

$18x - 9 - 10x = 63$

Step 1: Combine like terms $(18x - 10x) - 9 = 63 \implies 8x - 9 = 63$

Step 2: Solve for $x$ $8x = 63 + 9 \implies 8x = 72$ $x = \frac{72}{8} = 9$ So, $x = 9$.

Would you like further details or explanations on any step?

Here are 5 related questions to expand your understanding:

1. How do you solve linear equations with fractions?
2. What are the steps to simplify an equation before solving for $x$?
3. How can combining like terms help in solving equations faster?
4. Why do we multiply both sides of the equation to eliminate fractions?
5. How do you check if the solution to an equation is correct?

Tip: Always check your solutions by plugging the values of $x$ back into the original equations.