Write the absolute value equation if it has the following solutions. Hint: Your equation should be written as x−b =c. (Here b and c are some numbers.) a Two solutions: x=2, x=13.
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The absolute value equation is , if the equation has a two solutions of x=2 and x=13.

Step-by-step explanation:

The given is,

        Two solutions

                  x = 2

                  x = 13

Step:1

       We form the equation by the reverse method of Quadratic equation solve method,

        For first solution,

                                  x = 2

                            x - 2 = 0..............................(1)

        For second solution.    

                                 x = 13

                          x - 13 = 0..............................(2)

       From the equations (1) and (2)

                         ( x - 2 ) ( x - 13 ) = 0

      Multiply the equations,

Step:2

       Check for solution,

       Substitute the x value,

                                              0 = 0

Result:

          The absolute value equation is , if the equation has a two solutions of x=2 and x=13.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°