Question

|х – 3| – |2х– 4| = – 5.

Answer 1

Ответ:

-4;6

Объяснение:

х-3=0; х=3

2х-4=0; х=4/2; х=2

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1) х∈(-∞;2]

3-х+2х-4=-5

х=-4∈(-∞;2]

2)х∈(2;3)

3-х-2х+4=-5

-3х=-12

х=4∉(2;3)

3)х∈[3;+∞)

х – 3– 2х+4 = – 5

х=6∈[3;+∞)

Answer 2

To solve the equation |x - 3| - |2x - 4| = -5, you can break it down into cases based on the absolute values. The absolute value of a real number is non-negative, so there are four cases to consider:

Case 1: x - 3 is non-negative, and 2x - 4 is non-negative. Case 2: x - 3 is non-negative, and 2x - 4 is negative. Case 3: x - 3 is negative, and 2x - 4 is non-negative. Case 4: x - 3 is negative, and 2x - 4 is negative.

Let's examine each case:

Case 1: x - 3 ≥ 0 2x - 4 ≥ 0

Solve the inequalities: x ≥ 3 2x ≥ 4

Now, find the intersection of these solutions: x ≥ 3 (since 2x ≥ 4 implies x ≥ 2)

Case 2: x - 3 ≥ 0 2x - 4 < 0

Solve the inequalities: x ≥ 3 2x < 4

Now, find the intersection of these solutions: x ≥ 3 (since 2x < 4 implies x < 2)

Case 3: x - 3 < 0 2x - 4 ≥ 0

Solve the inequalities: x < 3 2x ≥ 4

Now, find the intersection of these solutions: x ≥ 2 (since 2x ≥ 4 implies x ≥ 2)

Case 4: x - 3 < 0 2x - 4 < 0

Solve the inequalities: x < 3 2x < 4

Now, find the intersection of these solutions: x < 3 (since 2x < 4 implies x < 2)

Now, let's combine the solutions from all the cases:

For Case 1: x ≥ 3 For Case 2: x ≥ 3 For Case 3: x ≥ 2 For Case 4: x < 3

To find the overall solution to the original equation, we need to consider all these cases. So, the solution is the union of these intervals:

x < 3 (from Case 4) x ≥ 2 (from Case 3) x ≥ 3 (from Cases 1 and 2)

Putting it all together, the solution is: x < 3 or x ≥ 2