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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], follow these steps:

1. Isolate the variable term:
- Start by eliminating the constant term on the left side. To do this, add 9 to both sides of the inequality:
[tex]\[ 5x - 9 + 9 \leq 21 + 9 \][/tex]
which simplifies to:
[tex]\[ 5x \leq 30 \][/tex]

2. Solve for the variable:
- Now, divide both sides of the inequality by 5 to isolate [tex]\(x\)[/tex]:
[tex]\[ \frac{5x}{5} \leq \frac{30}{5} \][/tex]
which simplifies to:
[tex]\[ x \leq 6 \][/tex]

Hence, the solution set for the inequality [tex]\(5x - 9 \leq 21\)[/tex] is:
[tex]\[ x \leq 6 \][/tex]

Among the given options, the correct answer is:
[tex]\[ x \leq 6 \][/tex]
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