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Which represents the solution of [tex]-9.5 + 6x \geq 42.1[/tex] using interval notation?

A. [tex](8.6, \infty)[/tex]
B. [tex][8.6, \infty)[/tex]
C. [tex](\infty, 8.6)[/tex]
D. [tex](\infty, 8.6][/tex]


Sagot :

To solve the inequality [tex]\(-9.5 + 6x \geq 42.1\)[/tex] and express the solution in interval notation, follow these steps:

1. Isolate the term involving [tex]\( x \)[/tex]:
Begin by adding 9.5 to both sides of the inequality to isolate the term involving [tex]\( x \)[/tex].
[tex]\[ -9.5 + 6x + 9.5 \geq 42.1 + 9.5 \][/tex]
Simplifying this, we get:
[tex]\[ 6x \geq 51.6 \][/tex]

2. Solve for [tex]\( x \)[/tex]:
Next, divide both sides of the inequality by 6 to solve for [tex]\( x \)[/tex]:
[tex]\[ \frac{6x}{6} \geq \frac{51.6}{6} \][/tex]
Simplifying this, we find:
[tex]\[ x \geq 8.6 \][/tex]

3. Express the solution in interval notation:
The solution [tex]\( x \geq 8.6 \)[/tex] means that [tex]\( x \)[/tex] can be any number greater than or equal to 8.6. In interval notation, this is represented as:
[tex]\[ [8.6, \infty) \][/tex]

Thus, the correct interval notation that represents the solution of [tex]\(-9.5 + 6x \geq 42.1\)[/tex] is [tex]\([8.6, \infty)\)[/tex]. Therefore, the correct choice among the given options is:
[tex]\[ [8.6, \infty) \][/tex]
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