Question

1. suppose c is between a and b. solve for x. explain your reasoning for the equation you set up.

ca = 2x + 5
bc = 3x - 7
ab = 10

Explanation:

Step1: Use segment - addition postulate

Since $C$ is between $A$ and $B$, we have $CA + BC=AB$. Substituting the given expressions, we get the equation $(2x + 5)+(3x - 7)=10$.

Step2: Simplify the left - hand side

Combine like terms: $(2x+3x)+(5 - 7)=10$, which simplifies to $5x-2 = 10$.

Step3: Isolate the variable term

Add 2 to both sides of the equation: $5x-2 + 2=10 + 2$, resulting in $5x=12$.

Step4: Solve for $x$

Divide both sides by 5: $x=\frac{12}{5}=2.4$.

Answer:

$x = 2.4$