francycastillo08
Answered

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Which represents the solution set of the inequality [tex]5x - 9 \leq 21[/tex]?

A. [tex]x \leq \frac{12}{5}[/tex]
B. [tex]x \geq \frac{12}{5}[/tex]
C. [tex]x \geq 6[/tex]
D. [tex]x \leq 6[/tex]

Sagot :

GinnyAnswer
To solve the inequality [tex]\( 5x - 9 \leq 21 \)[/tex], let's follow the steps systematically:

1. Start with the given inequality:

[tex]\( 5x - 9 \leq 21 \)[/tex]

2. Add 9 to both sides of the inequality to isolate the term with [tex]\( x \)[/tex]:

[tex]\[ 5x - 9 + 9 \leq 21 + 9 \][/tex]

Simplifying this results in:

[tex]\[ 5x \leq 30 \][/tex]

3. Divide both sides of the inequality by 5 to solve for [tex]\( x \)[/tex]:

[tex]\[ \frac{5x}{5} \leq \frac{30}{5} \][/tex]

Simplifying this gives:

[tex]\[ x \leq 6 \][/tex]

So, the solution set of the inequality [tex]\( 5x - 9 \leq 21 \)[/tex] is:

[tex]\[ x \leq 6 \][/tex]

Hence, the correct answer is [tex]\( \boxed{x \leq 6} \)[/tex].
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