Question

Solve the compound inequality y−1<2 and y+2≥1. Write the solution in set-builder notation.

Answer 1

The solution in set builder notation is given by = {y:3>y≥-1}

Given the inequalities are,

y-1<2 ............(i)

y+2 ≥ 1 ..............(ii)

Solving the first inequality we get,

y-1 < 2

y-1+1 < 2+1, adding 1 to both sides

y < 3

Solving second inequality we get,

y+2 ≥ 1

y+2-2 ≥ 1-2

y ≥ -1

So the range is 3>y≥-1

So the solution in set builder notation is = {y:3>y≥-1}

To know more about Inequality refer to:

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