Full solution

Q. Solve the inequality and graph the solution.

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4g - \frac{2}{5}(5g - 10) \geq 10

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Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Simplify left side: Simplify the left side of the inequality: $\newline$ $4g - \frac{2}{5}(5g - 10) \geq 10$ $\newline$ Distribute the $-\frac{2}{5}$ across $(5g - 10)$ : $\newline$ $4g - (\frac{2}{5} \times 5g) + (\frac{2}{5} \times 10) \geq 10$ $\newline$ $4g - 2g + 4 \geq 10$
Combine like terms: Combine like terms: $\newline$ $4g - 2g + 4 \geq 10$ $\newline$ $2g + 4 \geq 10$
Subtract to isolate $g$ : Subtract $4$ from both sides to isolate the term with $g$ : $2g + 4 - 4 \geq 10 - 4$ $2g \geq 6$
Divide to solve for g: Divide both sides by $2$ to solve for g: $\newline$ $\frac{2g}{2} \geq \frac{6}{2}$ $\newline$ $g \geq 3$
Graph solution: Graph the solution on a number line: $\newline$ Plot a closed circle at $g = 3$ and shade the line to the right, indicating $g$ is greater than or equal to $3$ .
Change endpoint: Select an endpoint to change from closed to open: $\newline$ Change the closed circle at $g = 3$ to an open circle to indicate $g$ is greater than $3$ .