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Which statement is true about this equation?
[tex]\[ -9(x+3)+12=-3(2x+5)-3x \][/tex]

A. The equation has one solution, [tex]\(x=1\)[/tex].

B. The equation has one solution, [tex]\(x=0\)[/tex].

C. The equation has no solution.

D. The equation has infinitely many solutions.

Sagot :

GinnyAnsweridn
To determine the correct statement about the given equation

[tex]\[ -9(x+3) + 12 = -3(2x+5) - 3x, \][/tex]

we can follow a step-by-step process to simplify and analyze the equation. Here are the steps:

1. Expand both sides of the equation:

- Left side:
[tex]\[ -9(x + 3) + 12 \implies -9x - 27 + 12 \implies -9x - 15 \][/tex]

- Right side:
[tex]\[ -3(2x + 5) - 3x \implies -6x - 15 - 3x \implies -9x - 15 \][/tex]

2. Set the simplified expressions equal to each other:
[tex]\[ -9x - 15 = -9x - 15 \][/tex]

3. Analyze the resulting equation:

Since both sides of the equation are exactly the same, this indicates that:

[tex]\[ -9x - 15 = -9x - 15 \][/tex]

This equation is true for all values of [tex]\( x \)[/tex]. It doesn't matter what [tex]\( x \)[/tex] is, the equation will always hold true because both sides are identical.

4. Conclusion:

Because the simplified forms are the same, the original equation has no constraint on [tex]\( x \)[/tex]; hence, it has infinitely many solutions.

Therefore, the correct answer is:
D. The equation has infinitely many solutions.
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