Question

Решите систему нервенств [3x-8>x-1 [x+9<2x

Answer 1

3x-x>-1+8
x-2x<-9

2x>7
-x<-9

x>3
x<9

Answer 2

Solving the System of Inequalities

To solve the system of inequalities 3x - 8 > x - 1 and x + 9 < 2x, we will follow these steps:

Step 1: Solve the first inequality, 3x - 8 > x - 1. Step 2: Solve the second inequality, x + 9 < 2x. Step 3: Determine the values of x that satisfy both inequalities.

Let's solve each inequality step by step.

Solving the First Inequality

The first inequality is 3x - 8 > x - 1.

To solve this inequality, we will isolate the variable x on one side of the inequality sign.

Step 1: Subtract x from both sides of the inequality: 3x - x - 8 > x - x - 1 simplifies to 2x - 8 > -1.

Step 2: Add 8 to both sides of the inequality: 2x - 8 + 8 > -1 + 8 simplifies to 2x > 7.

Step 3: Divide both sides of the inequality by 2: (2x)/2 > 7/2 simplifies to x > 7/2.

Therefore, the solution to the first inequality is x > 7/2.

Solving the Second Inequality

The second inequality is x + 9 < 2x.

To solve this inequality, we will isolate the variable x on one side of the inequality sign.

Step 1: Subtract x from both sides of the inequality: x - x + 9 < 2x - x simplifies to 9 < x.

Therefore, the solution to the second inequality is 9 < x.

Determining the Values of x that Satisfy Both Inequalities

To find the values of x that satisfy both inequalities, we need to find the intersection of the solution sets for each inequality.

From the first inequality, we know that x > 7/2.

From the second inequality, we know that 9 < x.

To satisfy both inequalities, x must be greater than 7/2 and also greater than 9.

Therefore, the solution to the system of inequalities is x > 9.

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