Solve for 

q

.

–

18

q

+

18

q

+

2

q

+

14

=

4

q

=

Let's simplify the given equation step by step:

\[
-18q + 18q + 2q + 14 = 4q
\]

1. Combine like terms on the left side:

\[
(-18q + 18q) + 2q + 14 = 4q
\]

Since \(-18q + 18q = 0\), we are left with:

\[
2q + 14 = 4q
\]

2. Now, subtract \(2q\) from both sides to isolate the variable:

\[
14 = 4q - 2q
\]

\[
14 = 2q
\]

3. Finally, divide both sides by 2 to solve for \(q\):

\[
q = \frac{14}{2} = 7
\]

Thus, the solution is \(q = 7\).

Would you like further clarification on any steps?

### Related questions:
1. What happens when the variable terms don’t cancel out like \( -18q + 18q \)?
2. How would you handle this equation if fractions were involved?
3. What is the role of the distributive property in solving equations?
4. How would this problem change if there were parentheses involved?
5. Can you explain how to check the solution by substituting back into the original equation?

**Tip:** Always double-check your solution by substituting it back into the original equation.

Learn how to solve the linear equation -18q + 18q + 2q + 14 = 4q with step-by-step guidance. This problem focuses on key algebraic concepts such as combining like terms and applying the properties of equality, suitable for students in Grades 6-8.

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