Question

question 8
point p is the midpoint of de, dp = 3x + 2, and de = 10x - 12.
what is the value of x?
hint: de is the whole distance and dp is equal to how much of the whole distance?
4
8
question 9

Explanation:

Step1: Use mid - point property

Since P is the mid - point of DE, then $DP=\frac{1}{2}DE$. So, $2DP = DE$.

Step2: Substitute given expressions

Substitute $DP = 3x + 2$ and $DE=10x - 12$ into $2DP = DE$. We get $2(3x + 2)=10x - 12$.

Step3: Expand left - hand side

Expand $2(3x + 2)$ using the distributive property: $6x+4 = 10x - 12$.

Step4: Move x terms to one side

Subtract $6x$ from both sides: $4=10x - 6x-12$, which simplifies to $4 = 4x-12$.

Step5: Isolate x

Add 12 to both sides: $4 + 12=4x$, so $16 = 4x$. Then divide both sides by 4: $x = 4$.

Answer:

4