Question

Розвяжи систему нерівностей -x+8>05x<-15​

Answer 1

$-x + 8 > 0\\-x > -8\\x < 8$

Ответ: x∈(-∞; 8).

$5x$

Ответ: x∈(-∞; -3).

Answer 2

Solving the System of Inequalities

To solve the system of inequalities -x + 8 > 0 and 5x < -15, we can follow these steps:

1. Solve the first inequality -x + 8 > 0 for x. 2. Solve the second inequality 5x < -15 for x. 3. Determine the values of x that satisfy both inequalities.

Solving the First Inequality

To solve the inequality -x + 8 > 0, we can isolate x by performing the following steps:

Step 1: Subtract 8 from both sides of the inequality: - -x > -8

Step 2: Multiply both sides by -1 to reverse the inequality: - x < 8

So, the solution to the first inequality is x < 8.

Solving the Second Inequality

To solve the inequality 5x < -15, we can isolate x by performing the following steps:

Step 1: Divide both sides by 5: - x < -3

So, the solution to the second inequality is x < -3.

Determining the Common Solution

Now, we need to find the values of x that satisfy both inequalities. Since both inequalities have the condition x <, the common solution is the intersection of the individual solutions. Therefore, the common solution is x < -3.

Conclusion

The solution to the system of inequalities -x + 8 > 0 and 5x < -15 is x < -3.