Question

solve for x.

Explanation:

Step1: Identify similar - triangles property

The two triangles $\triangle YXW$ and $\triangle YSR$ are similar. For similar triangles, the ratios of corresponding sides are equal. Since the lines $SR$ and $XW$ are parallel, we can use the mid - segment theorem (if $S$ and $R$ are mid - points of $YX$ and $WX$ respectively). Here, we can set up the proportion based on the fact that the ratio of the lengths of the parallel segments is equal. The length of the mid - segment $SR=\frac{1}{2}$ of the length of the base $XW$. So, $- 11 + 2x=\frac{1}{2}(x + 8)$.

Step2: Expand the equation

Multiply both sides of the equation $-11 + 2x=\frac{1}{2}(x + 8)$ by 2 to get rid of the fraction. We have $2(-11 + 2x)=x + 8$. Using the distributive property, $-22+4x=x + 8$.

Step3: Isolate the variable $x$

Subtract $x$ from both sides: $-22 + 4x-x=x + 8-x$, which simplifies to $-22+3x = 8$. Then add 22 to both sides: $-22+3x+22=8 + 22$, resulting in $3x=30$.

Step4: Solve for $x$

Divide both sides of the equation $3x = 30$ by 3. So, $\frac{3x}{3}=\frac{30}{3}$, and $x = 19$.

Answer:

$x = 19$