Question
8. Graph the solutions for the inequality: -3x + 1 ≤ - 47
Answers
GPT-4o mini
To graph the solutions for the inequality \(-3x + 1 \leq -47\), we first need to solve the inequality for \(x\).
### Step 1: Solve the inequality
1. Start with the inequality:
\[
-3x + 1 \leq -47
\]
2. Subtract \(1\) from both sides:
\[
-3x \leq -48
\]
3. Divide by \(-3\). Remember, when you divide or multiply both sides of an inequality by a negative number, you must flip the inequality sign:
\[
x \geq 16
\]
### Step 2: Graph the solution
To graph the solution \(x \geq 16\):
1. Draw a number line.
2. Plot a closed circle (or a filled dot) at \(16\) because the inequality is inclusive (\( \leq \)).
3. Shade the line to the right of \(16\) to indicate that all values greater than or equal to \(16\) are included in the solution.
The graph will show all the values of \(x\) that satisfy the inequality \(x \geq 16\).
### Step 1: Solve the inequality
1. Start with the inequality:
\[
-3x + 1 \leq -47
\]
2. Subtract \(1\) from both sides:
\[
-3x \leq -48
\]
3. Divide by \(-3\). Remember, when you divide or multiply both sides of an inequality by a negative number, you must flip the inequality sign:
\[
x \geq 16
\]
### Step 2: Graph the solution
To graph the solution \(x \geq 16\):
1. Draw a number line.
2. Plot a closed circle (or a filled dot) at \(16\) because the inequality is inclusive (\( \leq \)).
3. Shade the line to the right of \(16\) to indicate that all values greater than or equal to \(16\) are included in the solution.
The graph will show all the values of \(x\) that satisfy the inequality \(x \geq 16\).