Question

find ik
i •\t10\t2x + 23
\t\t\t• • k
\t\t\tj
|←\t\t\t\t\t\t x + 22\t\t\t→|

Explanation:

Step1: Set up the equation

From the number line, we know that \( IJ + JK = IK \). So, \( 10+(2x + 23)=x + 22 \).
Simplify the left - hand side: \( 10+2x+23=x + 22\), which becomes \(2x+33=x + 22\).

Step2: Solve for x

Subtract \(x\) from both sides of the equation \(2x+33=x + 22\):
\(2x - x+33=x - x+22\), so \(x+33 = 22\).
Then subtract 33 from both sides: \(x=22 - 33=- 11\).

Step3: Find the length of IK

We know that \(IK=x + 22\). Substitute \(x=-11\) into the expression for \(IK\):
\(IK=-11 + 22 = 11\).

Answer:

\(11\)