Question

1.) 7+7/9x=−42 2.) 4x+1=−15 3.)−4(x−3)=−40

Answer 1

Answer:

1) x= -1/27

2) x=-4

3) x=13

Step-by-step explanation:

1) 7+7/9x= = -42

   14/9x= = -42

  14/9x X 9x= -42 X 9x

    14= -378x

    -378x= 14

   -378x/-378= 14/-378

      x= -1/27

2) 4x+1=−15

 4x+1-1=-15-1

    4x=-16

   4x/4= -16/4

      x=-4

3) −4(x−3)=−40

 -4(x-3)/-4= -40/4

     x-3=10

   x-3+3=10+3

        x=13

Answer 2

(x2+
7
3 x−
17
3 )=3(x2+
7
3 x+
49
36 −
49
36 −
17
3 ) : x=−
7+√253
6 , x=
√253−7
6 (Decimal: x=−3.81766…, x=1.48432…)

(x2+
7
3 x−
17
3 )=3(x2+
7
3 x+
49
36 −
49
36 −
17
3 )

Expand 3(x2+
7
3 x+
49
36 −
49
36 −
17
3 ): 3x2+7x−17
x2+
7
3 x−
17
3 =3x2+7x−17
Add 17 to both sides
x2+
7
3 x−
17
3 +17=3x2+7x−17+17
Simplify
34
3 +
7
3 x+x2=3x2+7x
Subtract 7x from both sides
34
3 +
7
3 x+x2−7x=3x2+7x−7x
Simplify
x2−
14
3 x+
34
3 =3x2
Subtract 3x2 from both sides
x2−
14
3 x+
34
3 −3x2=3x2−3x2
Simplify
−2x2−
14x
3 +
34
3 =0

Solve with the quadratic formula
x1, 2=
−(−
14
3 )±√(−
14
3 )2−4(−2)
34
3
2(−2)

√(−
14
3 )2−4(−2)
34
3 =
2√253
3
x1, 2=
−(−
14
3 )±
2√253
3
2(−2)
Separate the solutions
x1=
−(−
14
3 )+
2√253
3
2(−2) , x2=
−(−
14
3 )−
2√253
3
2(−2)

x=
−(−
14
3 )+
2√253
3
2(−2) : −
7+√253
6

x=
−(−
14
3 )−
2√253
3
2(−2) :
√253−7
6
The solutions to the quadratic equation are:
X= — 7+/253. /253 — 7
______________ ,x = __________
6 6