Question

1. find the value of x given the following information.

• q is between p and r;
• pq = 5x - 10;
• qr = 3(x + 4); and
• pq ≅ qr.

p q r
5x - 10 3(x + 4)
x = _

Explanation:

Step1: Set up the equation

Since $PQ\cong QR$, we have $5x - 10=3(x + 4)$.

Step2: Expand the right - hand side

Using the distributive property $a(b + c)=ab+ac$, we get $5x-10 = 3x+12$.

Step3: Move the $x$ terms to one side

Subtract $3x$ from both sides: $5x-3x - 10=3x-3x + 12$, which simplifies to $2x-10 = 12$.

Step4: Move the constant terms to one side

Add 10 to both sides: $2x-10 + 10=12 + 10$, resulting in $2x=22$.

Step5: Solve for $x$

Divide both sides by 2: $\frac{2x}{2}=\frac{22}{2}$, so $x = 11$.

Answer:

$11$