Your friend says that the solutions to the inequality 5 x minus 15 x greater than or equals minus 20 are x greater than or equals 2. Solve the inequality correctly. What error did your friend​ make?
5 x minus 15 x
greater than or equals
negative 20
negative 10x
greater than or equals
negative 20
x
greater than or equals
2

Let's solve the inequality step by step and identify the error made.

### Given Inequality:
\[ 5x - 15x \geq -20 \]

### Step 1: Simplify the Left Side
Combine like terms on the left side:
\[ (5x - 15x) \geq -20 \]
\[ -10x \geq -20 \]

### Step 2: Solve for \( x \)
To isolate \( x \), divide both sides of the inequality by \(-10\). However, remember that dividing by a negative number reverses the inequality sign:
\[ x \leq \frac{-20}{-10} \]
\[ x \leq 2 \]

### Correct Solution:
The correct solution is \( x \leq 2 \).

### Error in Your Friend's Solution:
Your friend correctly simplified the inequality to \( -10x \geq -20 \) but made an error when solving for \( x \). They did not reverse the inequality sign when dividing by \(-10\), which led them to conclude \( x \geq 2 \) instead of the correct solution \( x \leq 2 \).

Would you like more details or have any questions?

### Relative Questions:
1. What is the rule for reversing the inequality sign?
2. How do you solve an inequality involving division by a negative number?
3. What are the steps to combine like terms in an inequality?
4. How does simplifying an inequality differ from simplifying an equation?
5. Can you explain why the inequality sign reverses when dividing by a negative number?

### Tip:
Always double-check the direction of the inequality sign when dividing or multiplying both sides by a negative number in inequalities.

Your friend says that the solutions to the inequality 5x - 15x ≥ -20 are x ≥ 2. Solve the inequality correctly. What error did your friend make?

Discover the correct method to solve the inequality 5x - 15x ≥ -20 and understand the common mistake made when dividing by a negative number. This problem is ideal for students in Grades 7-9 and covers essential algebraic concepts, including the properties of inequalities.

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