Question

Розв'яжіть систему нерівностей: {0.4х-1,3≥3,5-2х{7-1,3х≥-0,4-5х​ Смотреть ответ dashaa20006 dashaa20006 Відповідь: х є [2; +нескінченності)Пояснення: числа з х переносимо в одну сторону, без х в іншу

Answer 1

Solving the System of Inequalities

To solve the system of inequalities {0.4x - 1.3 ≥ 3.5 - 2x, 7 - 1.3x ≥ -0.4 - 5x}, we will solve each inequality separately and then find the intersection of their solution sets.

Let's start with the first inequality: 0.4x - 1.3 ≥ 3.5 - 2x.

1. Simplify the inequality: 0.4x - 1.3 ≥ 3.5 - 2x 0.4x + 2x ≥ 3.5 + 1.3 2.4x ≥ 4.8

2. Divide both sides of the inequality by 2.4 to solve for x: x ≥ 4.8 / 2.4 x ≥ 2

Now let's move on to the second inequality: 7 - 1.3x ≥ -0.4 - 5x.

1. Simplify the inequality: 7 - 1.3x ≥ -0.4 - 5x 1.3x - 5x ≥ -0.4 - 7 -3.7x ≥ -7.4

2. Divide both sides of the inequality by -3.7. Since we are dividing by a negative number, the inequality sign will flip: x ≤ -7.4 / -3.7 x ≤ 2

Now we have the solution sets for each inequality: - For the first inequality, x ≥ 2. - For the second inequality, x ≤ 2.

To find the intersection of these solution sets, we look for the values of x that satisfy both inequalities. In this case, the only value that satisfies both inequalities is x = 2.

Therefore, the solution to the system of inequalities {0.4x - 1.3 ≥ 3.5 - 2x, 7 - 1.3x ≥ -0.4 - 5x} is x = 2.

Note: The solution set is the interval [2, ∞) because x is greater than or equal to 2.