Respuesta :
Answer: No solution
Step-by-step explanation:
Let's solve the equation step by step:
4
�
−
2
�
+
8
=
2
(
2
�
+
6
)
4v−2v+8=2(2v+6)
First, let's simplify both sides of the equation:
On the left side, combine the terms:
(
4
�
−
2
�
)
+
8
=
2
�
+
8
(4v−2v)+8=2v+8
On the right side, distribute the 2:
2
(
2
�
+
6
)
=
4
�
+
12
2(2v+6)=4v+12
Now, our equation becomes:
2
�
+
8
=
4
�
+
12
2v+8=4v+12
To solve for
�
v, let's isolate the variable on one side:
Subtract
2
�
2v from both sides:
2
�
+
8
−
2
�
=
4
�
+
12
−
2
�
2v+8−2v=4v+12−2v
8
=
2
�
+
12
8=2v+12
Subtract 12 from both sides:
8
−
12
=
2
�
8−12=2v
−
4
=
2
�
−4=2v
Divide both sides by 2:
�
=
−
4
2
v=
2
−4
�
=
−
2
v=−2
Now, let's check if
�
=
−
2
v=−2 satisfies the original equation:
Original equation:
4
�
−
2
�
+
8
=
2
(
2
�
+
6
)
4v−2v+8=2(2v+6)
Substitute
�
=
−
2
v=−2:
4
(
−
2
)
−
2
(
−
2
)
+
8
=
2
(
2
(
−
2
)
+
6
)
4(−2)−2(−2)+8=2(2(−2)+6)
−
8
+
4
+
8
=
2
(
−
4
+
6
)
−8+4+8=2(−4+6)
−
4
=
2
(
2
)
−4=2(2)
−
4
=
4
−4=4
The equation
−
4
=
4
−4=4 is not true.
So, the solution
�
=
−
2
v=−2 does not satisfy the original equation.
Therefore, the equation has no solution.
Let's solve the equation step by step:
4
�
−
2
�
+
8
=
2
(
2
�
+
6
)
4v−2v+8=2(2v+6)
First, let's simplify both sides of the equation:
On the left side, combine the terms:
(
4
�
−
2
�
)
+
8
=
2
�
+
8
(4v−2v)+8=2v+8
On the right side, distribute the 2:
2
(
2
�
+
6
)
=
4
�
+
12
2(2v+6)=4v+12
Now, our equation becomes:
2
�
+
8
=
4
�
+
12
2v+8=4v+12
To solve for
�
v, let's isolate the variable on one side:
Subtract
2
�
2v from both sides:
2
�
+
8
−
2
�
=
4
�
+
12
−
2
�
2v+8−2v=4v+12−2v
8
=
2
�
+
12
8=2v+12
Subtract 12 from both sides:
8
−
12
=
2
�
8−12=2v
−
4
=
2
�
−4=2v
Divide both sides by 2:
�
=
−
4
2
v=
2
−4
�
=
−
2
v=−2
Now, let's check if
�
=
−
2
v=−2 satisfies the original equation:
Original equation:
4
�
−
2
�
+
8
=
2
(
2
�
+
6
)
4v−2v+8=2(2v+6)
Substitute
�
=
−
2
v=−2:
4
(
−
2
)
−
2
(
−
2
)
+
8
=
2
(
2
(
−
2
)
+
6
)
4(−2)−2(−2)+8=2(2(−2)+6)
−
8
+
4
+
8
=
2
(
−
4
+
6
)
−8+4+8=2(−4+6)
−
4
=
2
(
2
)
−4=2(2)
−
4
=
4
−4=4
The equation
−
4
=
4
−4=4 is not true.
So, the solution
�
=
−
2
v=−2 does not satisfy the original equation.
Therefore, the equation has no solution.
