Math Problem Statement

1. Чи правильно, що: 1) протилежним до числа |-3| є число -3; 2) протилежним до числа 4 є число -|4|? 2. Знайдіть відстань між точками: 1) A(4,5) і B(9-1/2); 2) C(-2,7) і D(0,2); 3) M(-2 1/2) і N(-4,5). 3. Розв'яжіть рівняння: 1) ||x| + 2| = 0; 2) ||x| - 5| = 0; 3) 4 - x | + 128 = 0; 4) | -x| + 3 = 125.

Solution

Let's solve the tasks step by step. The questions are written in Ukrainian, and I'll translate them while providing solutions:

1. Verify the truth of these statements:

  1. "The opposite of the number ∣−3∣|-3| is −3-3."

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Math Problem Analysis

Mathematical Concepts

Absolute Value
Distance Formula
Equations
Algebra

Formulas

Distance Formula: d = √[(x2 - x1)^2 + (y2 - y1)^2]
Equations involving absolute values: |x| = a implies x = ±a

Theorems

Absolute value property
Distance formula for two points in a plane

Suitable Grade Level

Grades 8-10

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