Question

|х-2|=-3 3|x|-1=0 2|x|+3=0 |3x+2|-4=0 2x-1+7=8

Answer 1

Объяснение:

1. |x-2| = -3  - x∈∅ (модуль всегда равен положительному числу)

2. 3|x| - 1 = 0;   3|x| = 1;   |x| = $\frac{1}{3}$;   x$_{1}$ = $\frac{1}{3}$;   x$_{2}$ = $-\frac{1}{3}$;

3. 2|x| + 3 = 0;   2|x| = -3  - x∈∅ (модуль всегда равен положительному числу)

4. |3x + 2| - 4 = 0;   |3x +2| = 4;

3x + 2 = 4;   3x = 2;   x$_{1}$ = $\frac{2}{3}$;

3x + 2 = -4;   3x = -6;  x$_{2}$ = -2;

5. 2x - 1 + 7 = 8;   2x - 8 = 8;   2x = 16;   x = 8;

Answer 2

It looks like you've provided a set of equations involving absolute value expressions. I'll help you solve each of these equations step by step.

1. |x - 2| = -3: Absolute values are always non-negative, so the absolute value of any expression cannot be negative. Therefore, there are no solutions for this equation.

2. 3|x| - 1 = 0: Add 1 to both sides: 3|x| = 1 Divide both sides by 3: |x| = 1/3 This gives two possible solutions: x = 1/3 and x = -1/3.

3. 2|x| + 3 = 0: Subtraction doesn't make sense with absolute values because they're always non-negative. Therefore, there are no solutions for this equation.

4. |3x + 2| - 4 = 0: Add 4 to both sides: |3x + 2| = 4 The absolute value of any expression can be equal to the positive value inside it or its negation. So we have two cases:

   Case 1: 3x + 2 = 4 Subtract 2 from both sides: 3x = 2 Divide both sides by 3: x = 2/3

   Case 2: 3x + 2 = -4 Subtract 2 from both sides: 3x = -6 Divide both sides by 3: x = -2

   So, the solutions are x = 2/3 and x = -2.

5. 2x - 1 + 7 = 8: Combine the constants on the left side: 2x + 6 = 8 Subtract 6 from both sides: 2x = 2 Divide both sides by 2: x = 1

In summary:

• The equation |x - 2| = -3 has no solutions.
• The equation 3|x| - 1 = 0 has solutions x = 1/3 and x = -1/3.
• The equation 2|x| + 3 = 0 has no solutions.
• The equation |3x + 2| - 4 = 0 has solutions x = 2/3 and x = -2.
• The equation 2x - 1 + 7 = 8 has a solution x = 1.