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How many solutions does the following equation have?

[tex]\[ 14(z+3) = 14z + 21 \][/tex]

Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(C) Infinitely many solutions

Sagot :

GinnyAnsweridn
To determine the number of solutions for the equation
[tex]\[ 14(z + 3) = 14z + 21, \][/tex]
we'll follow a detailed, step-by-step approach.

1. Expand the left-hand side of the equation:
[tex]\[ 14(z + 3) = 14z + 14 \cdot 3 \][/tex]
[tex]\[ = 14z + 42. \][/tex]
So, the equation now looks like:
[tex]\[ 14z + 42 = 14z + 21. \][/tex]

2. Next, we want to simplify the equation by isolating the variable term:
Subtract [tex]\( 14z \)[/tex] from both sides:
[tex]\[ 14z + 42 - 14z = 14z + 21 - 14z. \][/tex]
This simplifies to:
[tex]\[ 42 = 21. \][/tex]

3. Analyze the simplified equation:
[tex]\[ 42 = 21 \][/tex]
This statement is false, as 42 does not equal 21.

Since we've arrived at a false statement, it means that there are no values of [tex]\( z \)[/tex] that satisfy the given equation. Therefore, the equation has no solutions.

So, the final answer is:
(A) No solutions
Wegnerkolmp2741oidn

Answer:

(A) No solutions

Step-by-step explanation:

14(z+3) = 14z + 21

To solve, distribute the 14.

14z + 42 = 14z+21

Subtract 14z from each side.

14z-14z +42 = 14z-14z +21

42=21

Since this is not a true statement, there are no solutions.

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