Question

Solve the linear inequality, Enter the solution set of the Inequality in Interval notation Type "infinity" to represent [infinity], if needed. Type "negative infinity" or "Infinity" to represent -[infinity], i needed. Be sure to use appropriate symbols on the endpoints of the interval. Do not enter any spaces in your answer. 2y+1/5 - y-2/3 ≤ - 1/15

Answer 1

To solve the linear inequality 2y+1/5 - y-2/3 ≤ - 1/15, we need to combine like terms, find a common denominator, and isolate the variable. The solution is y ≥ -3/2.

Step-by-step explanation:

To solve the linear inequality 2y+1/5 - y-2/3 ≤ - 1/15, we need to combine like terms. Let's find a common denominator for 1/5 and 2/3, which is 15. Multiplying the fractions by their respective denominators, we get 6/15y + 3/15 - 10/15y - 10/15 ≤ - 1/15. Simplifying further, we have -4/15y - 7/15 ≤ - 1/15.

To isolate the variable, we need to get rid of the denominators. We can do this by multiplying both sides of the inequality by -15, which will give us (-15)(-4/15y - 7/15) ≥ (-15)(-1/15). Simplifying, we have 4y + 7 ≥ 1.

To solve for y, we subtract 7 from both sides, giving us 4y ≥ -6. Finally, we divide both sides by 4, resulting in y ≥ -3/2.

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