To determine which inequality Preston solved, we'll solve each inequality step-by-step and graph the solutions on a number line.
1. Solve the first inequality: \[ 2.1x + 5.6 \geq 8.75 \]
Step 1: Subtract 5.6 from both sides: \[ 2.1x \geq 8.75 - 5.6 \] \[ 2.1x \geq 3.15 \]
Step 2: Divide both sides by 2.1: \[ x \geq \frac{3.15}{2.1} \]
Calculating the right side: \[ \frac{3.15}{2.1} \approx 1.5 \]
Thus, the solution is: \[ x \geq 1.5 \]
2. Solve the second inequality: \[ 3.4x - 1.2 \geq 4.75 \]
Step 1: Add 1.2 to both sides: \[ 3.4x \geq 4.75 + 1.2 \] \[ 3.4x \geq 5.95 \]
Step 2: Divide both sides by 3.4: \[ x \geq \frac{5.95}{3.4} \]
Calculating the right side: \[ \frac{5.95}{3.4} \approx 1.75 \]
Thus, the solution is: \[ x \geq 1.75 \]
Summary of Solutions:
- For \( 2.1x + 5.6 \geq 8.75 \), the solution is \( x \geq 1.5 \).
- For \( 3.4x - 1.2 \geq 4.75 \), the solution is \( x \geq 1.75 \).
Now, if Preston graphed his solution on a number line, and if the graph shows a starting point at 1.5 and includes all numbers greater than or equal to 1.5, then he solved the first inequality. If the starting point on the graph is 1.75 or higher, then he solved the second inequality.
Conclusion: If you know the point at which the graph starts, you can identify which inequality he solved based on the starting number. If it's at 1.5 or above, it's the first. If it's at 1.75 or above, it's the second inequality.
1 answer