Solve 2x - 1 < 7 and 5x + 3 < 3. x < 0 x 0 < x < 4

Question

Solve 2x - 1 < 7 and 5x + 3 < 3. x x < 4 x

Answer 1

2x -1 <7 ; then, 2x < 8; then x < 4;
5x + 3 < 3; then, 5x < 0; then x < 0;
Finally, {x / x < 0};

Answer 2

Solution for givrn system of inequalities:
`\ ~x < 0\`

Explanation:

We are given a system of two inequalities:

`2x-1 < 7\\5x+3 < 3`

Solving the inequalities individually:

`2x-1 < 7\\2x<7+1\\2x < 8\\x < 4\\\text{In interval notation: } x \in (-\infty, 4) \\\\5x + 3 < 3\\5x < 3-3\\5x < 0\\x< 0\\\text{In interval notation: } x \in (-\infty, 0)`

The intersection of the two solution will give us the solution to the system of inequalities:

`x \in (-\infty, 4) \cap (-\infty, 0)\\ x \in (-\infty, 0) \\\ ~x < 0\`