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Alex_Xolod [135]
3 years ago
10

-| x-4| + 2 = -2x + 7

Mathematics
1 answer:
astraxan [27]3 years ago
7 0

X=3

Let's solve your equation step-by-step.

−

|

x

−

4

|

+

2

=

−

2

x

+

7

Step 1: Add -2 to both sides.

−

|

x

−

4

|

+

2

+

−

2

=

−

2

x

+

7

+

−

2

−

|

x

−

4

|

=

−

2

x

+

5

Step 2: Divide both sides by -1.

−

|

x

−

4

|

−

1

=

−

2

x

+

5

−

1

|

x

−

4

|

=

2

x

−

5

Step 3: Solve Absolute Value.

|

x

−

4

|

=

2

x

−

5

We know either

x

−

4

=

2

x

−

5

or

x

−

4

=

−

(

2

x

−

5

)

x

−

4

=

2

x

−

5

(Possibility 1)

x

−

4

−

2

x

=

2

x

−

5

−

2

x

(Subtract 2x from both sides)

−

x

−

4

=

−

5

−

x

−

4

+

4

=

−

5

+

4

(Add 4 to both sides)

−

x

=

−

1

−

x

−

1

=

−

1

−

1

(Divide both sides by -1)

x

=

1

x

−

4

=

−

(

2

x

−

5

)

(Possibility 2)

x

−

4

=

−

2

x

+

5

(Simplify both sides of the equation)

x

−

4

+

2

x

=

−

2

x

+

5

+

2

x

(Add 2x to both sides)

3

x

−

4

=

5

3

x

−

4

+

4

=

5

+

4

(Add 4 to both sides)

3

x

=

9

3

x

3

=

9

3

(Divide both sides by 3)

x

=

3

Check answers. (Plug them in to make sure they work.)

x

=

1

(Doesn't work in original equation)

x

=

3

(Works in original equation)

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What is the y-coordinate for the solution to the system of equations?<br><br> {y=1/2x−4<br> {y=−2x+1
katovenus [111]

Answer:

y = -3

Step-by-step explanation:

{y = x/2 - 4

y = 1 - 2 x

Substitute y = x/2 - 4 into the second equation:

{y = x/2 - 4

x/2 - 4 = 1 - 2 x

In the second equation, look to solve for x:

{y = x/2 - 4

x/2 - 4 = 1 - 2 x

Add 2 x + 4 to both sides:

{y = x/2 - 4

(5 x)/2 = 5

Multiply both sides by 2/5:

{y = x/2 - 4

x = 2

Substitute x = 2 into the first equation:

{y = -3

x = 2

Collect results in alphabetical order:

Answer:

{x = 2

y = -3

6 0
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