Question

1) |3х-6|=02) |х-4|=53) |2х+5|=54) |4х+5|=3​

Answer 1

Ответ:

1) 3х = 6

х = 6÷3

х = 2

2) х = 5 + 4

х = 9

3) 2х = 5 - 5

2х = 0

х = 0÷2

х = 0

4) 4х = 3 - 5

4х = -2

х = -0,5

Answer 2

Let's solve each of the absolute value equations step by step:

1. |3x - 6| = 0

Since the absolute value of any number is always non-negative, the only way for the absolute value to equal zero is if the expression inside the absolute value is zero itself.

3x - 6 = 0 3x = 6 x = 2

So the solution to this equation is x = 2.

2. |x - 4| = 5

For this equation, we can have two scenarios: either the expression inside the absolute value is positive or negative.

Scenario 1: x - 4 > 0 x > 4

In this case, the equation becomes: x - 4 = 5 x = 5 + 4 x = 9

Scenario 2: x - 4 < 0 x < 4

In this case, the equation becomes: -(x - 4) = 5 -x + 4 = 5 -x = 5 - 4 -x = 1 x = -1

So the solutions to this equation are x = 9 and x = -1.

3. |2x + 5| = 5

Again, we have two scenarios:

Scenario 1: 2x + 5 > 0 2x > -5 x > -5/2

In this case, the equation becomes: 2x + 5 = 5 2x = 0 x = 0

Scenario 2: 2x + 5 < 0 2x < -5 x < -5/2

In this case, the equation becomes: -(2x + 5) = 5 -2x - 5 = 5 -2x = 5 + 5 -2x = 10 x = -10/2 x = -5

So the solutions to this equation are x = 0 and x = -5.

4. |4x + 5| = 3

Again, we have two scenarios:

Scenario 1: 4x + 5 > 0 4x > -5 x > -5/4

In this case, the equation becomes: 4x + 5 = 3 4x = 3 - 5 4x = -2 x = -2/4 x = -1/2

Scenario 2: 4x + 5 < 0 4x < -5 x < -5/4

In this case, the equation becomes: -(4x + 5) = 3 -4x - 5 = 3 -4x = 3 + 5 -4x = 8 x = 8/-4 x = -2

So the solutions to this equation are x = -1/2 and x = -2.

To summarize:

1. x = 2
2. x = 9 or x = -1
3. x = 0 or x = -5
4. x = -1/2 or x = -2