Question

How do I do these problems?

Answer 1

Answer:

Step-by-step explanation:

$12.\ \frac{2}{3}x+2=16 < == subtract\ 2\ from\ both\ sides \\\\.\ \ \ \ \ \ \ \ -2 \ -2\\\frac{2}{3}x=14 < == multiply\ both\ sides\ by\ 3 \\\\3( \frac{2}{3}x=14)\\\\2x=42 < == divide\ both\ sides\ by\ 2\\/2 \ \ \ /2\\\\x=21 < == final\ answer$

Check your work:

$\frac{2}{3}x+2=16\\\\\frac{2}{3}(21)+2=16\\\\\frac{42}{3}+2=16\\\\14+2=16\\\\16=16$

This statement is correct

$13.\ \frac{x}{2} +\frac{x}{3} =\frac{5}{6} < == find\ the\ common\ denominator\ (6) \\\\\frac{3x}{6} +\frac{2x}{6} =\frac{5}{6} < == combine\ like\ terms \\\\\frac{5x}{6} =\frac{5}{6} < == divide\ both\ sides\ by\ \frac{5}{6} \\\\x=1 < == final\ answer$

Check your work:

$\frac{x}{2} +\frac{x}{3} =\frac{5}{6}\\\\\frac{1}{2} +\frac{1}{3} =\frac{5}{6}\\\\\frac{3}{6} +\frac{2}{6} =\frac{5}{6}\\\\\frac{5}{6}=\frac{5}{6}$

This statement is correct

$14.\ \frac{x-1}{6} -\frac{x+1}{8}=\frac{1}{12} < ==find\ the\ common\ denominator\ (24) \\\\\frac{24x-1}{6} -\frac{24x+1}{8}=\frac{24}{12}\\\\4(x-1) -3(x+1)=2 < ==distribute\\\\4(x)+4(-1) -3(x)+-3(1)=2\\\\4x-4-3x-3=2 < ==combine\ like\ terms\\\\x-7=2 < ==add\ 7\ to\ both\ sides\\\\.\ +7\ +7\\\\x =9 < == final\ answer$

Check your work:

$\frac{x-1}{6} -\frac{x+1}{8}=\frac{1}{12}\\\\\frac{9-1}{6} -\frac{9+1}{8}=\frac{1}{12}\\\\\frac{8}{6} -\frac{10}{8}=\frac{1}{12}\\\\\frac{32}{24}- \frac{30}{24}=\frac{1}{12}\\\\\frac{2}{24}=\frac{1}{12}\\\\\frac{1}{12}=\frac{1}{12}$

This statement is correct

$15.\ \frac{1}{4}+\frac{x+1}{8}=\frac{1}{2} < ==find\ the\ common\ denominator\ (8)\\\\\frac{8}{4}+\frac{8x+1}{8}=\frac{8}{2}\\\\2+x+1=4 < ==combine\ like\ terms\\\\3+x=4 < ==subtract\ 3\ from\ both\ sides\\\\-3\ \ \ -3\\\\x=1 < ==final\ answer$

Check your work:

$\frac{1}{4}+\frac{x+1}{8}=\frac{1}{2}\\\\\frac{1}{4}+\frac{1+1}{8}=\frac{1}{2}\\\\\frac{1}{4}+\frac{2}{8}=\frac{1}{2}\\\\\frac{1}{4}+\frac{1}{4}=\frac{1}{2}\\\\\frac{2}{4}=\frac{1}{2}\\\\\frac{1}{2}=\frac{1}{2}$

This statement is correct

Hope this helps!