No.143 Inequalities with Fractions
POINT
Multiply both sides by the positive least common multiple of the denominators to clear fractions, then solve the inequality.
Example
Solve the following inequalities.
1
\(\frac{x+1}{2}<\frac{x+7}{3}\)
\(x<11\)
2
\(\frac{2x-1}{3}\geq x+2\)
\(x\leq-7\)
TRY
Solve the following inequalities.
TRY 1
\(\frac{x+2}{3}>2\)
\(x>4\)
TRY 2
\(\frac{x-1}{4}\leq2\)
\(x\leq9\)
TRY 3
\(\frac{x+3}{2}<\frac{x+9}{3}\)
\(x<9\)
TRY 4
\(\frac{2x+1}{3}\geq\frac{x+2}{2}\)
\(x\geq4\)
TRY 5
\(\frac{x-2}{5}>\frac{x+1}{2}\)
\(x<-3\)
TRY 6
\(\frac{3x-1}{4}\leq\frac{x+2}{2}\)
\(x\leq5\)