Question

2 which of the following equations have the same solution? circle three equations. 2n = 15 n + 8.4 = 15.9 3n = 25.5 -7 + n = 0.5 n - 7 = -0.5

Explanation:

Step 1: Solve \(2n = 15\)

To find \(n\), divide both sides by 2: \(n=\frac{15}{2}=7.5\)

Step 2: Solve \(n + 8.4=15.9\)

Subtract 8.4 from both sides: \(n = 15.9 - 8.4 = 7.5\)

Step 3: Solve \(3n = 25.5\)

Divide both sides by 3: \(n=\frac{25.5}{3}=8.5\) (Wait, no, 25.5 ÷ 3: 3×8 = 24, 25.5 - 24 = 1.5, 1.5÷3 = 0.5, so 8 + 0.5 = 8.5? Wait, no, wait 15×1.7 = 25.5? Wait, no, earlier \(2n=15\) gives \(n = 7.5\). Wait, maybe I made a mistake. Wait, 3n = 25.5: 25.5 divided by 3. Let's do 25.5 ÷ 3. 3×7 = 21, 25.5 - 21 = 4.5, 4.5 ÷ 3 = 1.5, so 7 + 1.5 = 8.5? No, that's wrong. Wait, 7.5×3 = 22.5, not 25.5. Wait, maybe the third equation is different? Wait, no, let's check the fourth equation: \(-7 + n = 0.5\). Add 7 to both sides: \(n = 0.5 + 7 = 7.5\). And the fifth equation: \(n - 7=-0.5\). Add 7 to both sides: \(n=-0.5 + 7 = 6.5\). Wait, so let's recalculate:

Wait, \(2n = 15\): \(n = 15/2 = 7.5\)

\(n + 8.4 = 15.9\): \(n = 15.9 - 8.4 = 7.5\)

\(3n = 25.5\): \(n = 25.5 / 3 = 8.5\) (Wait, 3×8.5 = 25.5, correct. So that's 8.5, not 7.5. Then \(-7 + n = 0.5\): \(n = 0.5 + 7 = 7.5\)

\(n - 7=-0.5\): \(n = -0.5 + 7 = 6.5\)

Wait, so the equations with \(n = 7.5\) are \(2n = 15\), \(n + 8.4 = 15.9\), and \(-7 + n = 0.5\)? Wait, but the problem says to circle three equations. Wait, maybe I miscalculated \(3n = 25.5\). Wait, 7.5×3 = 22.5, 8.5×3 = 25.5. So that's 8.5. Then the three equations with the same solution (7.5) are \(2n = 15\), \(n + 8.4 = 15.9\), and \(-7 + n = 0.5\). Wait, let's check \(-7 + n = 0.5\): \(n = 7.5\), correct. \(n - 7=-0.5\): \(n = 6.5\), incorrect. \(3n = 25.5\): \(n = 8.5\), incorrect. So the three equations with solution \(n = 7.5\) are \(2n = 15\), \(n + 8.4 = 15.9\), and \(-7 + n = 0.5\). Wait, but let's confirm again:

1. \(2n = 15\): \(n = 7.5\)
2. \(n + 8.4 = 15.9\): \(n = 7.5\)
3. \(3n = 25.5\): \(n = 8.5\) (wrong)
4. \(-7 + n = 0.5\): \(n = 7.5\) (correct)
5. \(n - 7 = -0.5\): \(n = 6.5\) (wrong)

So the three equations with the same solution (7.5) are \(2n = 15\), \(n + 8.4 = 15.9\), and \(-7 + n = 0.5\)

Answer:

The three equations with the same solution (\(n = 7.5\)) are:

• \(2n = 15\)
• \(n + 8.4 = 15.9\)
• \(-7 + n = 0.5\)