--1,8< 1 - 7 x <36

To solve the compound inequality \(-1.8 < 1 - 7x < 36\), we can break it down into two separate inequalities:

1. \(-1.8 < 1 - 7x\)
2. \(1 - 7x < 36\)

Step 1: Solve the first inequality \(-1.8 < 1 - 7x\)

1. Subtract 1 from both sides: \[ -1.8 - 1 < -7x \] \[ -2.8 < -7x \]

2. Divide both sides by -7 (remember to reverse the inequality sign when dividing by a negative number): \[ \frac{-2.8}{-7} > x \] \[ 0.4 > x \quad \text{or} \quad x < 0.4 \]

Step 2: Solve the second inequality \(1 - 7x < 36\)

1. Subtract 1 from both sides: \[ -7x < 36 - 1 \] \[ -7x < 35 \]

2. Divide both sides by -7 (again, reverse the inequality sign): \[ x > \frac{35}{-7} \] \[ x > -5 \]

Step 3: Combine the results

From the two inequalities, we have:

• \(x < 0.4\)
• \(x > -5\)

Thus, the solution to the compound inequality is: \[ -5 < x < 0.4 \]

This means \(x\) can take any value between -5 and 0.4, not including -5 and 0.4 themselves.