Question

1. solve for x. 6x + 7 19x - 28

Explanation:

Step1: Identify similar - triangles property

Since the two triangles are similar (by the AA - similarity criterion as the sides are parallel), the ratios of corresponding sides are equal. The marked sides are in proportion. So, we can set up the equation based on the property of similar - triangles: $\frac{6x + 7}{19x-28}=\frac{1}{2}$ (assuming the smaller triangle's side is half of the larger triangle's corresponding side based on the markings).

Step2: Cross - multiply

Cross - multiplying the equation $\frac{6x + 7}{19x-28}=\frac{1}{2}$ gives us $2(6x + 7)=19x-28$.
Expand the left - hand side: $12x+14 = 19x-28$.

Step3: Isolate the variable x

Subtract $12x$ from both sides: $14=19x - 12x-28$.
Simplify to get $14 = 7x-28$.
Add 28 to both sides: $14 + 28=7x$, so $42 = 7x$.
Divide both sides by 7: $x=\frac{42}{7}=6$.

Answer:

$x = 6$