Question

Solve (x + 1 < 5) ∩ (x - 4 > -3).

x < 4 or x > 1
1 < x < 4
{all real numbers}

Answer 1

{all real numbers}

Explanation:

Solve (x + 1 < 5) ∩ (x - 4 > -3).

For the expression

x + 1 < 5

Subtract 1 from both sides

x+1-1 < 5-1

x < 4

For the inequality

x - 4 > -3

Add 4 to both sodes

x-4+4 > -3 + 4

x > -1

Hence the intersection of both is on all real numbers since the value of x is greater than -1.