Question

How do I solve this?

Answer 1

Answer:

$x>\frac{83}{15}$

Step-by-step explanation:

STEP 1: Simplify $\frac{x-5}{2} +\frac{2}{5}>\frac{2}{3}$

$\frac{5x-21}{10}>\frac{2}{3}$

STEP 2: Multiply both sides of the equation by $10$.

$\frac{5x-21}{10}>\frac{2}{3}*(10)$

STEP 3: Remove parentheses.

$\frac{5x-21}{10}>\frac{2}{3}*(10)$

STEP 4: Multiply $\frac{2}{3}*(10)$

$\frac{5x-21}{10}>\frac{20}{3}$

STEP 5: Move all terms not containing $x$ to the right side of the inequality.

$5x>\frac{83}{3}$

STEP 6: Divide each term by $5$ and simplify.

$x>\frac{83}{15}$

STEP 7: The result can be shown in multiple forms.

Inequality Form:

$x>\frac{83}{15}$

Interval Notation:

$(\frac{83}{15}$,∞$)$

Answer 2

Answer:

x > $\frac{83}{15}$

Step-by-step explanation:

Given

$\frac{x-5}{2}$ + $\frac{2}{5}$ > $\frac{2}{3}$

Multiply through by 30 ( the LCM of 2, 5 and 3 ) to clear the fractions

15(x - 5) + 12 > 20 ← distribute and simplify left side

15x - 75 + 12 > 20

15x - 63 > 20 ( add 63 to both sides )

15x > 83 ( divide both sides by 15 )

x > $\frac{83}{15}$