Solve the following inequality for $$ q $$. Write your answer in simplest form. $$ -8 q-(-7 q+5)

Question

Solve the following inequality for $$ q $$. Write your answer in simplest form. $$ -8 q-(-7 q+5)<-4 q+10+3 $$

UpStudy AI · Accepted Answer

To solve the inequality:

$$
-8 q - (-7 q + 5) < -4 q + 10 + 3
$$

**Step 1: Simplify Both Sides**

1. **Left Side:**
$$
-8 q - (-7 q + 5) = -8 q + 7 q - 5 = -q - 5
$$

2. **Right Side:**
$$
-4 q + 10 + 3 = -4 q + 13
$$

So, the inequality becomes:
$$
-q - 5 < -4 q + 13
$$

**Step 2: Solve for $$ q $$**

1. **Add $$ 4 q $$ to both sides:**
$$
- q + 4 q - 5 < 13
$$
$$
3 q - 5 < 13
$$

2. **Add $$ 5 $$ to both sides:**
$$
3 q < 18
$$

3. **Divide both sides by $$ 3 $$:**
$$
q < 6
$$

**Final Answer:**
$$
q < 6
$$
$$ q < 6 $$

Solve the following inequality for . Write your answer in simplest form.