$q(x)=\frac{1}{2}x-3$q(x)=12​x−3​ ;   $q(x)=-4$q(x)=−4​


You provided the equation:

\[
q(x) = \frac{1}{2}x - 3
\]
and you are given $ q(x) = -4 $.

We need to solve for $ x $ in this equation:

\[
\frac{1}{2}x - 3 = -4
\]

### Step-by-step solution:

1. Start by isolating $ \frac{1}{2}x $. Add 3 to both sides of the equation:

\[
\frac{1}{2}x = -4 + 3
\]
\[
\frac{1}{2}x = -1
\]

2. Now, eliminate the fraction by multiplying both sides of the equation by 2:

\[
x = -1 \times 2
\]
\[
x = -2
\]

### Final Answer:
\[
x = -2
\]

Do you need more details on any step or have any further questions?

Here are some related questions:
1. What if $ q(x) = 0 $, how would we solve it?
2. How do we solve if the equation was $ q(x) = \frac{1}{4}x - 3 $?
3. How does multiplying both sides by 2 help in eliminating fractions?
4. Can we solve this equation graphically?
5. What happens if $ q(x) = 5 $?

**Tip:** When solving equations with fractions, multiplying both sides by the denominator simplifies the process.

Learn how to solve the linear equation q(x) = 1/2x - 3 when q(x) = -4 with a step-by-step solution. This example illustrates key concepts in algebra, focusing on solving for variables and manipulating linear equations. Ideal for students in Grades 6-8.

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