Distributive Property Practice AK

  1. $-30$
  2. $5b-15$
  3. $18$ 
  4. $-12b+96$
  5. $8m-12$
  6. $-18+6r$
  7. $-3w+4$
  8. $-2p+8$ 
  9. $-40$
  10. $4n-2$
  11. $z=4$

    $\eqalign{4(z-3)&=4\\4z-12&=4\\+12&=+12\\4z&=16\\\dfrac{4z}{4}&=\dfrac{16}{4}\\z=4}$
  12. $x=-3$

    $\eqalign{-7(x+2)&=7\\-7x-14&=7\\+14&=+14\\-7x&=21\\\dfrac{-7x}{-7}&=\dfrac{21}{-7}\\x&=-3}$
  13. $w=0$

    $\eqalign{\dfrac{1}{2}(w-3)&=-\dfrac{3}{2}\\\dfrac{1}{2}w-\dfrac{3}{2}&=-\dfrac{3}{2}\\+\dfrac{3}{2}&=+\dfrac{3}{2}\\\dfrac{1}{2}w&=0\\\dfrac{1}{2}w\times\dfrac{2}{1}&=0\times\dfrac{2}{1}\\w&=0}$
  14. $w=1$

    $\eqalign{5(3w-2)&=5\\15w-10&=5\\\quad+10&=+10\\15w&=15\\\dfrac{15w}{15}&=\dfrac{15}{15}\\w&=1}$
  15. $x=-\dfrac{1}{2}$

    $\eqalign{10(3x+2)&=5\\10x+20&=5\\\quad-20&=-20\\30x&=-15\\\dfrac{30x}{30}&=\dfrac{-15}{30}\\w&=-\dfrac{1}{2}}$
  16.  $y=-.75$

    $\eqalign{.5(1-4y)&=2\\.5-2y&=2\\-.5\quad\quad\;&=-.5\\-2y&=1.5\\\dfrac{-2y}{-2}&=\dfrac{1.5}{-2}\\y&=-.75}$
  17.  $x=-1$

    $\eqalign{7(5+(-8x))&=91\\35+(-56x)&=91\\-35\quad\quad\quad\quad\;\;&=-35\\-56x&=56\\\dfrac{-56x}{-56}&=\dfrac{56}{-56}\\x&=-1}$ 
  18. $x=2\dfrac{1}{3}$ OR $x=\dfrac{7}{3}$

    $\eqalign{\dfrac{3}{4}(2x+\dfrac{2}{3})&=4\\\dfrac{6}{4}x+\dfrac{6}{12}&=4\\\dfrac{3}{2}x+\dfrac{1}{2}&=4\\-\dfrac{1}{2}&=-\dfrac{1}{2}\\\dfrac{3}{2}x&=\dfrac{7}{2}\\\dfrac{3}{2}w\times\dfrac{2}{3}&=\dfrac{7}{2}\times\dfrac{2}{3}\\x&=\dfrac{7}{3}}$
  19. $q=-2$

    $\eqalign{15(2q+\dfrac{1}{3}q)&=-70\\30q+5q&=-70\\35q&=-70\\\dfrac{35q}{35}&=\dfrac{-70}{35}\\q&=-2}$
  20. $r=8$

    $\eqalign{\dfrac{3}{2}(\dfrac{1}{2}r-6)&=\dfrac{1}{4}r-5\\\dfrac{3}{4}r-\dfrac{18}{2}&=\dfrac{1}{4}r-5\\\dfrac{3}{4}r-9&=\dfrac{1}{4}r-5\\-\dfrac{1}{4}r+9&=-\dfrac{1}{4}r+9\\\dfrac{1}{2}r&=4\\\dfrac{1}{2}w\times\dfrac{2}{1}&=4\times2\\r&=8}$