Question

Please help? solve for variable and simplify each expression

Answer 1

$11.\\3d-2(8d-9)=-2d-4\qquad\text{use distributive property}\ a(b+c)=ab+ac\\\\3d+(-2)(8d)+(-2)(-9)=-2d-4\\\\3d-16d+18=-2d-4\qquad\text{combine like terms}\\\\(3d-16d)+18=-2d-4\qquad\text{subtract 18 from both sides}\\\\-13d=-2d-22\qquad\text{add 2d to both sides}\\\\-11d=-22\qquad\text{divide both sides by (-11)}\\\\\boxed{d=2}$

$13.\\3x-6=2+4(x-2)\qquad\text{use distributive property}\ a(b+c)=ab+ac\\\\3x-6=2+(4)(x)+(4)(-2)\\\\3x-6=2+4x-8\qquad\text{combine like terms}\\\\3x-6=4x+(2-8)\\\\3x-6=4x-6\qquad\text{add 6 to both sides}\\\\3x=4x\qquad\text{subtract 3x from both sides}\\\\\boxed{x=0}$

$15.\\2(x-3)=3(2x+2)\qquad\text{use distributive property}\ a(b+c)=ab+ac\\\\(2)(x)+(2)(-3)=(3)(2x)+(3)(2)\\\\2x-6=6x+6\qquad\text{add 6 to both sides}\\\\2x=6x+12\qquad\text{subtract 6x from both sides}\\\\-4x=12\qquad\text{divide both sides by (-4)}\\\\\boxed{x=-3}$

$17.\\3b+4-12b+6+2b\qquad\text{combine like terms}\\\\=(3b-12b+2b)+(4+6)\\\\=\boxed{-7b+10}$

$19.\\\dfrac{2^3}{2^3}=\dfrac{8}{8}=\boxed{1}$