Given the linear inequality 4 x + 2 3 y ≥ 6 4x+\frac23y\ge6 , determine if the following ordered pair is a solution to the inequality. ( 2 , 3 ) (2,3)

This problem gives us a linear inequality and asks us to determine if the following ordered pair is a solution to the inequality. Well, I know that my ordered pair is given in the form So I just need to replace the x's and y's in my inequality to see if it holds true. So we're going to have four times, and then in this case my x is two, plus two thirds times my y which is three, and that's going to be greater than or equal to six. Now four times two is eight. Now two thirds times three is just going to give us two, the threes will cancel, it's going to be greater than or equal to six. Eight plus two is 10. Now is this true? Is 10 greater than or equal to six? Well yes this is a true statement. 10 is greater than six. So in this case we would say that this is a solution to the linear inequality. So this is a solution, and that would be the answer to this. So we're asked if this is a solution, so we could just say, yes. This is a solution. Hope you found this helpful.

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Beginning & Intermediate Algebra

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Linear Inequalities in Two Variables

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Given the linear inequality $4 x plus two thirds y is greater than or equal to 6$ , determine if the following ordered pair is a solution to the inequality.
$open paren 2 comma 3 close paren$

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Start with the given inequality: $4x + \frac{2}{3}y \ge 6$.

Substitute the values of the ordered pair $(2, 3)$ into the inequality, where $x = 2$ and $y = 3$.

Calculate the left side by evaluating $4(2) + \frac{2}{3}(3)$.

Simplify the expression: $4 \times 2 = 8$ and $\frac{2}{3} \times 3 = 2$, so the left side becomes $8 + 2$.

Compare the simplified left side to the right side of the inequality, $6$, to check if $8 + 2 \ge 6$ holds true.

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Given the linear inequality $4 x plus two thirds y is greater than or equal to 6$ , determine if the following ordered pair is a solution to the inequality.
$open paren 2 comma 3 close paren$