Question

use the diagram below to solve for x and find the length of the indicated segment.
x=, ih=
i 2x - 2 h x + 4 g
23

Explanation:

Step1: Set up equation

Since $IH + HG=IG$, we have $(2x - 2)+(x + 4)=23$.

Step2: Simplify left - hand side

Combine like terms: $2x-2+x + 4=3x+2$. So the equation becomes $3x+2 = 23$.

Step3: Solve for x

Subtract 2 from both sides: $3x=23 - 2=21$. Then divide both sides by 3: $x=\frac{21}{3}=7$.

Step4: Find length of IH

Substitute $x = 7$ into the expression for $IH$. $IH=2x-2=2\times7-2=14 - 2=12$.

Answer:

$x = 7$, $IH=12$