Solve for a Variable Practice AK

1.

$\eqalign{x+2&=4\\x&=2}$

2.

$\eqalign{x+7&=13\\x&=6}$

3.

$\eqalign{x-3&=6\\x&=9}$

4.

$\eqalign{2-x&=43\\x&=-41}$

5.

$\eqalign{8-x&=-55\\x&=63}$

6.

$\eqalign{x+7&=-1\\-8}$

7.

$\eqalign{3x+2&=14\\x&=4}$

8.

$\eqalign{3-2x&=6\\x&=\dfrac{3}{-2}}$

9.

$\eqalign{\dfrac{x}{2}+2&=4\\\dfrac{x}{2}&=2\\x&=4}$

10.

$\eqalign{\dfrac{5}{x}-4&=16\\\dfrac{5}{x}&=20\\5&=20x\\x&=\dfrac{5}{20}\\x&=\dfrac{1}{4}}$

11.

$\eqalign{7x-8&=50\\x&=\dfrac{58}{7}}$

12.

$\eqalign{-16-\dfrac{x}{3}&=14\\-\dfrac{x}{3}&=30\\-x&=90\\x&=-90}$

13.

$\eqalign{9+\dfrac{4}{x}&=3\\\dfrac{4}{x}&=-6\\4&=-6x\\x&=\dfrac{4}{-6}=\dfrac{-2}{3}}$

14.

$\eqalign{12x-18&=-14\\12x&=4\\x&=\dfrac{1}{3}}$

15.

$\eqalign{\dfrac{4}{x}-19&=30\\\dfrac{4}{x}&=49\\\\4&=49x\\x&=\dfrac{4}{49}}$

16.

$\eqalign{\sqrt{x}&=9\\(\sqrt{x})^2&=9^2\\x&=81}$

17.

$\eqalign{\sqrt{x-5}&=8\\\sqrt{x-5}^2&=8^2\\x-5&=64\\x&=69}$

18.

$\eqalign{\sqrt{2x-4}-6&=6\\\sqrt{2x-4}-6+6&=6+6\\\sqrt{2x-4}&=12\\\sqrt{2x-4}^2&=12^2\\2x-4&=144\\2x-4+4&=144+4\\2x&=148\\x&=74}$

19.

$\eqalign{2\sqrt{-3x+19}+8&=16\\2\sqrt{-3x+19}&=8\\\dfrac{2\sqrt{-3x+19}}{2}&=\dfrac{8}{2}\\\sqrt{-3x+19}&=4\\\sqrt{-3x+19}^2&=4^2\\-3x+19&=16\\-3x+19-19&=16-19\\-3x&=-3\\x&=1}$

20.

$\eqalign{x^2&=36\\\sqrt{x^2}&=\sqrt{36}\\x&=\pm6}$

21.

$\eqalign{x^2-9&=40\\x^2-9+9&=40+9\\x^2&=49\\\sqrt{x^2}&=\sqrt{49}\\x&=\pm7} $

22.

$\eqalign{(x-7)^2+8&=89\\(x-7)^2+8-8&=89-8\\(x-7)^2&=81\\\sqrt{(x-7)^2}&=\sqrt{81}\\x-7&=\pm9}$ 
$\eqalign{x-7&=9 \;\;\;\;\;\;\;\;\;\;\;\;\;\; x&&-7&&&=-9\\x&=16  &&x&&&=-2}$

23.

$\eqalign{(2x-12)^2-5&=-1\\(2x-12)^2-5+5&=-1+5\\(2x-12)^2&=4\\\sqrt{(2x-12)^2}&=\sqrt{4}\\2x-12&=\pm2}$ 
$\eqalign{2x-12&=2 \;\;\;\;\;\;\;\;\;\;\;\;\;\; &&2x-12&&&=-2\\2x-12+12&=2+12  &&2x-12+12&&&=-2+12\\2x&=14 &&2x&&&=10\\x&=7 &&x&&&=5}$