-| x-4| + 2 = -2x + 7 Determine the real solution and the extraneous solution of the absolute value
equation.

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)

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.

step-by-step explanation:

is their an equation anywhere i can take a   look at it and see if i am right.