4x-3 (x -2y) + 1/2 (6x - 8y)

4x+2y

Step-by-step explanation:

4x-3(x-2y)+1/2x(6x-8y)

remove parentheses

Factor

4x-3x+6y+ 1/2*2(3x - 4y)

Reduce the numbers

4x-3x+6y+(3x - 4y)

remove parentheses

4x-3x+6y+3x - 4y

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.