Question

Solve the inequality
-(3x+3)-2x>-4(x-2)-2
Solve the inequality
5x-3(x+6) ≥8-(x-7)
Question 3 options:
What is the second step in solving the following inequality?
-(3x+3)-2x>-4(x-2)-2
Division Property of Inequality
Addition Property of Inequality
Distributive Property
Combine Like Terms

Solve for x
y<mx+b

solve for y
ax+by≤c

Answer 1

Let's solve each of your questions step by step.

### **Inequality 1:**
Solve the inequality:
\[
-(3x+3) - 2x > -4(x-2) - 2
\]

**Step 1: Distribute on both sides:**
Distributing gives us:
\[
-3x - 3 - 2x > -4x + 8 - 2
\]

**Step 2: Combine Like Terms:**
Combine like terms on both sides:
\[
-5x - 3 > -4x + 6
\]

### **What is the second step in solving the inequality?**
In this case, the second step is combining like terms after distributing. The appropriate option is:
- **Combine Like Terms**

### **Inequality 2:**
Solve the inequality:
\[
5x - 3(x + 6) \geq 8 - (x - 7)
\]

**Step 1: Distribute on both sides:**
\[
5x - 3x - 18 \geq 8 - x + 7
\]

**Step 2: Combine Like Terms:**
On the left side:
\[
2x - 18 \geq 15 - x
\]

**Step 3: Add x to both sides:**
\[
2x + x - 18 \geq 15
\]

**Step 4: Combine Like Terms again:**
\[
3x - 18 \geq 15
\]

### **Step 5: Add 18 to both sides:**
\[
3x \geq 33
\]

### **Step 6: Divide by 3:**
\[
x \geq 11
\]

### **Solve for y in terms of x:**
Given \( y < mx + b \):
To express \( y \) in terms of \( x \):
\[
y < mx + b
\]
This is already solved for \( y \).

Given \( ax + by \leq c \):
To solve for \( y \):
1. Move \( ax \) to the right side:
\[
by \leq c - ax
\]
2. Divide by \( b \) (assuming \( b \neq 0 \)):
\[
y \leq \frac{c - ax}{b}
\]

If \( b \) is negative, you must reverse the inequality sign:
\[
y \geq \frac{c - ax}{b}
\]

### **Final Summary:**
1. The second step in the first inequality is **Combine Like Terms.**
2. The inequality \( x \geq 11 \) is the solution for the second inequality.
3. \( y \) is solved from \( y < mx + b \) and rearranged from \( ax + by \leq c \) to \( y \leq \frac{c - ax}{b} \).