Question

A) 2x -10 < 0,x + 4 > 5;(5y - 4 > 6,4-y<3.​

Answer 1

2x-10 < 0

2x < 0+10

2x < 10

x < 10:2

x < 5

x+4 > 5

x > 5-4

x > 1

5y-4 > 6

5y > 6+4

5y > 10

y > 10:5

y > 2

4-y < 3

-y < 3-4

-y < -1

y > 1

Answer 2

To solve the system of inequalities, let's take it step by step. We have two pairs of inequalities:

A) 2x - 10 < 0 and x + 4 > 5 B) 5y - 4 > 6 and 4 - y < 3

Let's start with A):

1. 2x - 10 < 0

To solve for x, add 10 to both sides of the inequality:

2x - 10 + 10 < 0 + 10

2x < 10

Now, divide both sides by 2:

2x/2 < 10/2

x < 5

So the first solution for A) is x < 5.

2. x + 4 > 5

Subtract 4 from both sides:

x + 4 - 4 > 5 - 4

x > 1

The second solution for A) is x > 1.

Now let's move on to B):

3. 5y - 4 > 6

Add 4 to both sides:

5y - 4 + 4 > 6 + 4

5y > 10

Divide both sides by 5:

5y/5 > 10/5

y > 2

The first solution for B) is y > 2.

4. 4 - y < 3

Subtract 4 from both sides:

4 - y - 4 < 3 - 4

-y < -1

Multiply both sides by -1 (remember to flip the inequality when multiplying by a negative number):

-y * -1 > -1 * -1

y > 1

The second solution for B) is y > 1.

So, the solutions to the system of inequalities are as follows:

A) x < 5 and x > 1 B) y > 2 and y > 1

To summarize the solutions:

• For A), x must be between 1 and 5, exclusive.
• For B), y must be greater than both 1 and 2.

Therefore, the combined solution for the system is:

x > 1 and x < 5 and y > 2.