Question

1286. 2-x<3x-10 7x-1>x+5​

Answer 1

• Первое неравенство:

2 - x < 3x - 10

-x - 3x < -10 - 2

-4x < -12

x > 3

Ответ: x > 3

• Второе неравенство:

7x - 1 > x + 5

7x - x > 5 + 1

6x > 6

x > 1

Ответ: x > 1

Answer 2

To solve the inequalities:

1. 2 - x < 3x - 10
2. 7x - 1 > x + 5

We'll solve each inequality separately.

Inequality 1: 2 - x < 3x - 10

First, let's isolate the variable x. We can do this by adding x to both sides and adding 10 to both sides:

2 - x + x < 3x - 10 + x + 10

2 < 4x

Now, divide both sides by 4 (remember to reverse the inequality when dividing by a negative number):

2/4 < 4x/4

1/2 < x

So the solution for the first inequality is x > 1/2.

Inequality 2: 7x - 1 > x + 5

First, let's isolate the variable x. We can do this by subtracting x from both sides and adding 1 to both sides:

7x - 1 - x > x + 5 - x + 1

6x - 1 > 6

Now, add 1 to both sides:

6x - 1 + 1 > 6 + 1

6x > 7

Now, divide both sides by 6:

6x/6 > 7/6

x > 7/6

So the solution for the second inequality is x > 7/6.

To find the solution for both inequalities combined, we need to consider the intersection of the solutions, which means we take the values that satisfy both inequalities. Since both inequalities have x > 7/6 in common, the solution to the system of inequalities is:

x > 7/6.