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Find the solutions of the inequality

[tex]\[ \frac{2}{3} x - 5 \ \textgreater \ 7 \][/tex]

A. [tex]\( x \ \textless \ 18 \)[/tex]

B. [tex]\( x \ \textgreater \ 6 \)[/tex]

C. [tex]\( x \ \textgreater \ 18 \)[/tex]

D. [tex]\( x \ \textless \ 6 \)[/tex]



Answer :

GinnyAnswer
To solve the inequality [tex]\(\frac{2}{3} x - 5 > 7\)[/tex], follow these steps:

1. Isolate the variable [tex]\(x\)[/tex]:

Start by adding 5 to both sides of the inequality to eliminate the constant term on the left-hand side:
[tex]\[ \frac{2}{3} x - 5 + 5 > 7 + 5 \][/tex]
Simplifying this, we get:
[tex]\[ \frac{2}{3} x > 12 \][/tex]

2. Eliminate the fraction:

Multiply both sides of the inequality by [tex]\(\frac{3}{2}\)[/tex] to cancel out the fraction on the left-hand side:
[tex]\[ x > 12 \times \frac{3}{2} \][/tex]
Calculate the multiplication:
[tex]\[ x > 18 \][/tex]

Thus, the solution to the inequality [tex]\(\frac{2}{3} x - 5 > 7\)[/tex] is:
[tex]\[ x > 18 \][/tex]

3. Evaluate the given options:

- [tex]\(x < 18\)[/tex]: This does not satisfy [tex]\(x > 18\)[/tex].
- [tex]\(x > 6\)[/tex]: This is true for values greater than 6, but not necessarily greater than 18.
- [tex]\(x > 18\)[/tex]: This matches our solution.
- [tex]\(x < 6\)[/tex]: This is not true for values greater than 18.

Therefore, the correct solution among the given choices is:
[tex]\[ x > 18 \][/tex]

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