Question

PLEASE HELP Which expression is equivalent? 8 − 5(3x − 7)

A) 15x + 43 B) 9x − 21 C) −9x + 21 D) −15x + 43
Which expression is equivalent? 6(2x + 3) − 4(5x + 2)
A) 8x + 10 Eliminate B) 8x − 10 C) −8x + 10 D) −8x − 10 Which is equivalent to the expression? 4(x + 5) + 4x + 8
A) 4(2x + 7) B) 5x + 17 C) 8(x + 4) D) 8x + 13

Answer 1

Q1. D) -15x + 43

Q2. C) -8x + 10

Q3. A) 4(2x + 7)

Explanation:

`Q1:\\8-5(3x-7)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=8-(5)(3x)+(-5)(-7)=8-15x+35=-15x+(8+35)\\=\boxed{-15x+43}`

`Q2:\\6(2x+3)-4(5x+2)\qquad\text{use the distributive property}\\\\=(6)(2x)+(6)(3)+(-4)(5x)+(-4)(2)=12x+18-20x-8\\\\\text{combine like terms}\\\\=(12x-20x)+(18-8)=\boxed{-8x+10}`

`Q3.\\4(x+5)+4x+8\qquad\text{use the distributive property}\\\\=(4)(x)+(4)(5)+4x+8=4x+20+4x+8\\\\\text{combine like terms}\\\\=(4x+4x)+(20+8)=\boxed{8x+28}=(4)(2x)+(4)(7)=\boxed{4(2x+7)}`