Questions: Solve the following linear equation. Identify the equation as an identity, contradiction, or conditional equation. 3(y+1)-6(y-3)=9 y+21-12 y Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is . (Type an integer or a simplified fraction.) B. The solution is all real numbers. C. The solution is the empty set. State whether the equation is an identity, contradiction, or conditional equation. Identity Contradiction Conditional equation

Solve the following linear equation. Identify the equation as an identity, contradiction, or conditional equation. 3(y+1)-6(y-3)=9 y+21-12 y Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is . (Type an integer or a simplified fraction.) B. The solution is all real numbers. C. The solution is the empty set. State whether the equation is an identity, contradiction, or conditional equation. Identity Contradiction Conditional equation
Transcript text: Solve the following linear equation. Identify the equation as an identity, contradiction, or conditional equation. \[ 3(y+1)-6(y-3)=9 y+21-12 y \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \{ $\square$ \}. (Type an integer or a simplified fraction.) B. The solution is all real numbers. C. The solution is the empty set. State whether the equation is an identity, contradiction, or conditional equation. Identity Contradiction Conditional equation
failed

Solution

failed
failed

Solution Steps

To solve the given linear equation, we will first simplify both sides of the equation by distributing and combining like terms. Then, we will attempt to isolate the variable \( y \) to determine if there is a specific solution, if the equation holds for all values of \( y \), or if there is no solution. Based on the result, we will classify the equation as an identity, contradiction, or conditional equation.

Step 1: Expand the Equation

First, we need to expand the given linear equation:

\[ 3(y+1) - 6(y-3) = 9y + 21 - 12y \]

Expanding each term:

  • \(3(y+1) = 3y + 3\)
  • \(-6(y-3) = -6y + 18\)

Substituting these into the equation, we have:

\[ 3y + 3 - 6y + 18 = 9y + 21 - 12y \]

Step 2: Simplify Both Sides

Now, let's simplify both sides of the equation:

Left side:

\[ 3y + 3 - 6y + 18 = -3y + 21 \]

Right side:

\[ 9y + 21 - 12y = -3y + 21 \]

Step 3: Compare Both Sides

After simplification, the equation becomes:

\[ -3y + 21 = -3y + 21 \]

Both sides of the equation are identical, which means the equation holds true for all values of \(y\).

Step 4: Determine the Type of Equation

Since the equation is true for all values of \(y\), it is an identity.

Final Answer

The solution is all real numbers, and the equation is an identity.

\[ \boxed{\text{B. The solution is all real numbers.}} \]

\[ \boxed{\text{Identity}} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Which rule is a recursive rule for the sequence 1,-6,36,-216, ... ? an=6 cdot an-1 an=-6 cdot an-1 an=-1/6 cdot an-1 an=1/6 cdot an-1
failedAnswered
A data set on Shark Attacks Worldwide posted on StatCrunch records data on all shark attacks in recorded history including attacks before 1800. Variables contained in the data include time of attack, date, location, activity the victim was engaged in when attacked, whether or not the injury was fatal, and species of shark. Which of the following questions could not be answered using the data set?
failedAnswered
Multiple Choice Question A company's margin of safety calculation is an indication of how closely the company is operating relative to its fixed expenses its breakeven point its sales performance its operating income
failedAnswered
Express the answers to the following operations with the proper number of significant figures. A. 1.2 × 1.216 B. 3.000 / 2.0 C. (1.201 × 10^3) × (1.2 × 10^-2) D. 1.6+1.15 E. (41.314-41.03) × 1.23 F. 1.8+1.022+0.001 G. (0.050-0.0012) × (3.0-2.495)
failedAnswered
Identifiers Rules for identifiers A name created by a programmer for an item like a variable or method is called an identifier. An identifier must: - be a sequence of letters (a-z, A-Z), underscore (-), dollar signs (), and digits (0-9) - start with a letter, underscore, or dollar sign Note that "-", called an underscore, and "", called a dollar sign or currency symbol, are considered to be letters. A good practice followed by many Java programmers is to not use or in programmer-created identifiers. Identifiers are case sensitive, meaning upper and lower case letters differ. So numCats and NumCats are different. A reserved word is a word that is part of the language, like int, short, or double. A reserved word is also known as a keyword. A programmer cannot use a reserved word as an identifier. Many language editors will automatically color a program's reserved words. A list of reserved words appears at the end of this section. Check if the following identifiers are valid: c, cat, n1m1, short1, hello, 42c, hi there, and cat!