Question

Solve for x:
1 1/5x−2 1/3<1/7x+1 1/2

Answer 1

Answer: $x<3\frac{175}{222}$

Step-by-step explanation:

$1\frac{1}{5}x-2\frac{1}{3}<\frac{1}{7}x+1\frac{1}{2}$

Add $2\frac{1}{3}$ on both sides and subtract $\frac{1}{7}x$ on both sides to leave x's on the left side and independent values on the right.

$(2\frac{1}{3}-\frac{1}{7}x) +1\frac{1}{5}x-2\frac{1}{3}<\frac{1}{7}x+1\frac{1}{2}+(2\frac{1}{3}-\frac{1}{7}x)$

$1\frac{1}{5}x-\frac{1}{7}x<1\frac{1}{2}+2\frac{1}{3}$

Solve the fractions.

$1(\frac{1}{5}-\frac{1}{7})x<1+2(\frac{1}{2}+\frac{1}{3})$

$1(\frac{(1)(7)-(5)(1)}{(5)(7)} )x<3(\frac{(1)(3)+(2)(1)}{(2)(3)} )$

$1(\frac{7-5}{35} )x<3(\frac{3+2}{6} )$

$1(\frac{2}{35} )x<3(\frac{5}{6})$

$1\frac{2}{35}x<3\frac{5}{6}$

Convert the mixed fraction $1\frac{2}{35}$ to an improper fraction. You can do this by multiplying 1 times 35 and adding 2.

$\frac{37}{35}x<3\frac{5}{6}$

Now use the reciprocal (inverse fraction) and multiply on both sides to isolate x.

$(\frac{35}{37}) (\frac{37}{35})x <(3\frac{5}{6})(\frac{35}{37})$

$x<3(\frac{5}{6}*\frac{35}{37})$

$x<3(\frac{175}{222} )$

$x<3\frac{175}{222}$