Question

6x-3(x-1)больше или равно2+5x линейное неравенство.ПОМОГИТЕ ПОЖАЛУЙСТА очень очень нужно))))

Answer 1

6х-3(х-1) бир 2+5х
6х-3х+3 бир 2+5х
3х-5х бир 2-3
-2х бир -1
х мир 0,5
бир-больше или равно
мир-меньше или равно

Answer 2

Solving the Linear Inequality

To solve the linear inequality 6x - 3(x - 1) ≥ 2 + 5x, we can follow these steps:

1. Simplify both sides of the inequality: - Distribute the -3 to the terms inside the parentheses: 6x - 3x + 3 ≥ 2 + 5x. - Combine like terms: 3x + 3 ≥ 2 + 5x.

2. Move all the x terms to one side of the inequality and the constant terms to the other side: - Subtract 3x from both sides: 3 ≥ 2 + 2x. - Subtract 2 from both sides: 1 ≥ 2x.

3. Divide both sides of the inequality by 2 to solve for x: - Divide by 2: 1/2 ≥ x.

Therefore, the solution to the inequality is x ≤ 1/2.

Verification of the Solution

To verify the solution, we can substitute different values of x into the original inequality and check if the inequality holds true.

Let's substitute x = 0 into the inequality: - Left side: 6(0) - 3(0 - 1) = 0 - 3(-1) = 0 - (-3) = 0 + 3 = 3. - Right side: 2 + 5(0) = 2 + 0 = 2.

Since 3 is not less than or equal to 2, the inequality does not hold true for x = 0.

Now let's substitute x = 1/2 into the inequality: - Left side: 6(1/2) - 3(1/2 - 1) = 3 - 3(1/2 - 1) = 3 - 3(1/2 - 2/2) = 3 - 3(-1/2) = 3 - (-3/2) = 3 + 3/2 = 9/2. - Right side: 2 + 5(1/2) = 2 + 5/2 = 4/2 + 5/2 = 9/2.

Since 9/2 is equal to 9/2, the inequality holds true for x = 1/2.

Therefore, the solution x ≤ 1/2 is verified.

Conclusion

The solution to the linear inequality 6x - 3(x - 1) ≥ 2 + 5x is x ≤ 1/2. This means that any value of x less than or equal to 1/2 will satisfy the inequality.