Decide whether the equation is an identity, a conditional equation, or a contrad

Anonym

Anonym

Answered question

2021-09-24

Decide whether the equation is an identity, a conditional equation, or a contradiction. give the solution set.
12(x-2)=2(6x+1)-26

Answer & Explanation

Ezra Herbert

Ezra Herbert

Skilled2021-09-25Added 99 answers

Step 1 
Given: 
The equation is 12(x-2) = 2(6x+1)-26. 
Step 2 
Calculation: 
Make the provided equation as straightforward as possible.

12(x-2) = 2(6x+1)-26 
utilize the distribution property,

12(x)- 12(2) = 2(6x)+2(1)-26 
12x-24 = 12x+2-26 
12x-24 = 12x-24 
Step 3 
Subtract 12x on both sides, 
12x-24-12x = 12x-24-12x 
-24 =-24 
It appears to be an identity solution.
Step 4 
Answer: 
The solution set of the given equation is the set of all real numbers.

alenahelenash

alenahelenash

Expert2023-06-10Added 556 answers

Starting with the given equation:
12(x2)=2(6x+1)26
First, we can simplify both sides of the equation:
12x24=12x+226
Next, let's simplify further by combining like terms:
12x24=12x24
Now, let's analyze the equation. We observe that the variable terms on both sides, 12x, cancel out, leaving us with a constant term equation:
24=24
Since the constant terms on both sides are equal, the equation is an identity.
The solution set for an identity equation is all real numbers, as any value substituted for the variable would yield true equality.
Therefore, the solution set for the equation 12(x2)=2(6x+1)26 is (all real numbers).
star233

star233

Skilled2023-06-10Added 403 answers

Answer:
{x} (all real numbers)
Explanation:
Given:
12(x2)=2(6x+1)26
First, distribute the values inside the parentheses:
12x24=12x+226
Simplifying further, we can combine like terms:
12x24=12x24
Notice that both sides of the equation are identical. This means that the equation is an identity. In other words, any value of x will satisfy the equation.
{Solution Set: }{x}
The solution set indicates that the equation is true for any real value of x.
karton

karton

Expert2023-06-10Added 613 answers

Step 1: Distribute and simplify both sides of the equation:
12x24=12x+226
Step 2: Combine like terms:
12x24=12x24
Step 3: Subtract 12x from both sides of the equation:
24=24
The equation simplifies to 24=24, which means both sides are equal. Therefore, the equation is an identity.
The solution set for this equation is {x}, which represents all real numbers.

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