Question

-1 < или = 5-3x < или = 1

Answer 1

$- 1 \leqslant 5 - 3x \leqslant 1 \\ - 1 - 5 \leqslant - 3x \leqslant 1 - 5\\ - 6 \leqslant - 3x \leqslant - 4 \\ \frac{4}{3} \leqslant x \leqslant 2$

Answer 2

To solve the compound inequality -1 < 5-3x ≤ 1, we'll break it down into two separate inequalities and then find the solution for each inequality.

1. -1 < 5-3x: Subtract 5 from both sides of the inequality: -1 - 5 < 5 - 5 - 3x -6 < -3x

Now, divide both sides by -3, remembering to reverse the inequality since we are dividing by a negative number: -6 / -3 > x 2 > x or x < 2

2. 5-3x ≤ 1: Subtract 5 from both sides of the inequality: 5 - 5 - 3x ≤ 1 - 5 -3x ≤ -4

Now, divide both sides by -3, again remembering to reverse the inequality: -3x / -3 ≥ -4 / -3 x ≥ 4/3

So the two separate inequalities are:

1. x < 2
2. x ≥ 4/3

Now, let's represent the combined solution for the compound inequality: x < 2 OR x ≥ 4/3

This means that the values of x that satisfy the original compound inequality are all real numbers that are less than 2, or greater than or equal to 4/3.