What is the solution to StartFraction 5 over 6 EndFraction x minus one-third greater-than 1 and one-third?

Mathematics

2 answers:

Vikentia [17]3 years ago

6 0

Answer:

The correct answer is x > 2.

Step-by-step explanation:

$\dfrac{5}{6} x - \dfrac{1}{3} > 1\dfrac{1}{3}$

An inequality compares two quantities unlike an equality. An inequality is written with either a greater than ( > ) or lower than ( < ) or greater than equal to ( $\geq$ ) or less than equal to ( $\leq$ ) signs. We solve the above given inequality to find the solutions of the unknown x.

$\dfrac{5}{6} x - \dfrac{1}{3} > 1\dfrac{1}{3} \\\dfrac{5}{6} x - \dfrac{1}{3} > \dfrac{4}{3} \\\dfrac{5}{6} x > \dfrac{1}{3} + \dfrac{4}{3} \\\dfrac{5}{6} x > \dfrac{5}{3}\\x > 2$

Firstly we change the right hand side quantity to fraction.

We then transfer the - $\frac{1}{3}$ to the right hand side and add them. The inequality sign does not change as we are simply adding or subtracting terms from both the ends.

Finally we divide both sides with $\frac{6}{5}$ to get the required solution. The inequality sign does not change as we are multiplying both the ends with a positive quantity.