Question

j, k, and l are points on the same segment, and k is between j and l. 14. jk = 10, jl = 19, kl = ? 15. jk = kl and jl = 24, jk = ? 16. jl = 30, jk = 3x + 4, kl = 10x, x = ?, jk = ? 17. jl = 50 - 2x, jk = x + 7, kl = 3x + 1, jk = ?

Explanation:

Step1: Use segment - addition postulate

Since \(J\), \(K\), and \(L\) are collinear and \(K\) is between \(J\) and \(L\), then \(JL=JK + KL\).

Step2: Solve problem 14

Given \(JK = 10\) and \(JL=19\), substitute into \(JL=JK + KL\). We get \(19=10 + KL\). Then \(KL=JL - JK=19 - 10 = 9\).

Step3: Solve problem 15

Given \(JK = KL\) and \(JL = 24\), substitute into \(JL=JK + KL\). Since \(JK = KL\), then \(JL=JK+JK = 2JK\). So \(2JK=24\), and \(JK=\frac{24}{2}=12\).

Step4: Solve problem 16

Substitute into \(JL=JK + KL\). We have \(30=(3x + 4)+10x\). Combine like - terms: \(30 = 13x+4\). Subtract 4 from both sides: \(13x=30 - 4=26\). Divide both sides by 13: \(x = 2\). Then \(JK=3x + 4=3\times2+4=6 + 4 = 10\).

Step5: Solve problem 17

Substitute into \(JL=JK + KL\). We get \(50-2x=(x + 7)+(3x + 1)\). Combine like - terms: \(50-2x=4x + 8\). Add \(2x\) to both sides: \(50=6x + 8\). Subtract 8 from both sides: \(6x=50 - 8 = 42\). Divide both sides by 6: \(x = 7\). Then \(JK=x + 7=7 + 7=14\).

Answer:

1. 9
2. 12
3. \(x = 2\), \(JK = 10\)
4. 14