Question

2)3(x + 8) > 9 - 2x,3(x + 4) > x + 5.​

Answer 1

Пошаговое объяснение:

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Answer 2

To solve the system of inequalities:

1. 3(x + 8) > 9 - 2x
2. 3(x + 4) > x + 5

You can follow these steps:

1. Solve each inequality separately.

For the first inequality: 3(x + 8) > 9 - 2x

First, distribute the 3 on the left side: 3x + 24 > 9 - 2x

Now, isolate the x terms on one side and the constants on the other side: 3x + 2x > 9 - 24 5x > -15

Divide both sides by 5: x > -3

So the solution for the first inequality is x > -3.

For the second inequality: 3(x + 4) > x + 5

First, distribute the 3 on the left side: 3x + 12 > x + 5

Now, isolate the x terms on one side and the constants on the other side: 3x - x > 5 - 12 2x > -7

Divide both sides by 2: x > -7/2

So the solution for the second inequality is x > -7/2.

2. Now, we need to find the intersection of the two solutions. To do that, we take the intersection of the solution sets, which means we consider where both inequalities are simultaneously true.

The solutions are:

• For the first inequality: x > -3
• For the second inequality: x > -7/2

The intersection of these two solution sets is the set of values that satisfy both inequalities. To find the intersection, we take the greater of the two lower bounds:

x > max(-3, -7/2)

max(-3, -7/2) is -3 because -3 is the greater of the two values.

So, the solution to the system of inequalities is: x > -3