Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To determine how many solutions exist for the equation [tex]\(6 - 3x = 4 - x - 3 - 2x\)[/tex], we will follow these steps:
1. Simplify both sides of the equation:
Start by combining like terms on the right-hand side of the equation:
[tex]\[ 4 - x - 3 - 2x = 4 - 3 - x - 2x = 1 - 3x \][/tex]
Now, rewrite the equation with the simplified right-hand side:
[tex]\[ 6 - 3x = 1 - 3x \][/tex]
2. Isolate the variable [tex]\(x\)[/tex]:
To isolate the variable [tex]\(x\)[/tex], move all terms involving [tex]\(x\)[/tex] to one side of the equation and constant terms to the opposite side. However, in this case, both sides already contain the term [tex]\(-3x\)[/tex].
Subtract [tex]\(-3x\)[/tex] from both sides of the equation:
[tex]\[ 6 - 3x + 3x = 1 - 3x + 3x \][/tex]
Simplifying both sides:
[tex]\[ 6 = 1 \][/tex]
3. Analyze the resulting statement:
The resulting equation [tex]\(6 = 1\)[/tex] is a false statement. This indicates an inconsistency, meaning there is no value of [tex]\(x\)[/tex] that can satisfy the original equation.
Therefore, the original equation [tex]\(6 - 3x = 4 - x - 3 - 2x\)[/tex] has no solutions. The correct answer is:
D. No solutions
1. Simplify both sides of the equation:
Start by combining like terms on the right-hand side of the equation:
[tex]\[ 4 - x - 3 - 2x = 4 - 3 - x - 2x = 1 - 3x \][/tex]
Now, rewrite the equation with the simplified right-hand side:
[tex]\[ 6 - 3x = 1 - 3x \][/tex]
2. Isolate the variable [tex]\(x\)[/tex]:
To isolate the variable [tex]\(x\)[/tex], move all terms involving [tex]\(x\)[/tex] to one side of the equation and constant terms to the opposite side. However, in this case, both sides already contain the term [tex]\(-3x\)[/tex].
Subtract [tex]\(-3x\)[/tex] from both sides of the equation:
[tex]\[ 6 - 3x + 3x = 1 - 3x + 3x \][/tex]
Simplifying both sides:
[tex]\[ 6 = 1 \][/tex]
3. Analyze the resulting statement:
The resulting equation [tex]\(6 = 1\)[/tex] is a false statement. This indicates an inconsistency, meaning there is no value of [tex]\(x\)[/tex] that can satisfy the original equation.
Therefore, the original equation [tex]\(6 - 3x = 4 - x - 3 - 2x\)[/tex] has no solutions. The correct answer is:
D. No solutions
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.