Question

solve for x.
9)
10)
11)
12)

Explanation:

Problem 9

Step1: Use the mid - segment theorem

In a triangle, the mid - segment (a segment connecting the mid - points of two sides of a triangle) is parallel to the third side and half its length. Here, \(QR\) is the mid - segment of \(\triangle WXY\). So, \(2(2x - 3)=x + 9\)

Step2: Expand the left - hand side

$$
LATEXBLOCK0
$$

Step3: Subtract \(x\) from both sides

$$
LATEXBLOCK1
$$

Step4: Add 6 to both sides

$$
LATEXBLOCK2
$$

Step5: Divide both sides by 3

$$
LATEXBLOCK3
$$

Step1: Use the mid - segment theorem

In \(\triangle SRT\), \(CB\) is the mid - segment. So, \(2(x + 19)=x + 29\)

Step2: Expand the left - hand side

$$
LATEXBLOCK0
$$

Step3: Subtract \(x\) from both sides

$$
LATEXBLOCK1
$$

Step4: Subtract 38 from both sides

$$
LATEXBLOCK2
$$

Step1: Use the mid - segment theorem

In \(\triangle SQR\), \(ZY\) is the mid - segment. So, \(2(x + 2)=3x - 8\)

Step2: Expand the left - hand side

$$
LATEXBLOCK0
$$

Step3: Subtract \(2x\) from both sides

$$
LATEXBLOCK1
$$

Step4: Add 8 to both sides

$$
LATEXBLOCK2
$$

Answer:

\(x = 5\)

Problem 10