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Question 3 of 5

How many solutions does [tex]6 - 3x = 4 - x - 3 - 2x[/tex] have?

A. Two solutions
B. One solution
C. Infinitely many solutions
D. No solutions

Sagot :

GinnyAnswer
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
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