Which graph represents the solutions to this inequality: 5n−3<3(n+1)
To find the graph that represents the solutions to the inequality, it is necessary to first simplify the inequality. Starting with 5n - 3 < 3(n + 1), you can distribute the 3 through the parentheses to get 5n - 3 < 3n + 3.
To solve this inequality, you need to isolate the variable on one side of the inequality symbol. Begin by subtracting 3n from both sides: 5n - 3 - 3n < 3n + 3 - 3n, which simplifies to 2n - 3 < 3. Next, add 3 to both sides: 2n - 3 + 3 < 3 + 3, resulting in 2n < 6. Finally, divide both sides of the inequality by 2: 2n/2 < 6/2, giving n < 3.
This inequality can be represented on a number line by graphing an open circle at 3 and shading to the left, indicating that n is less than but not equal to 3. Therefore, the correct graph that represents the solution to 5n - 3 < 3(n + 1) is option C.
To find the graph that represents the solutions to the inequality 5n - 3 < 3(n + 1), we can start by simplifying the equation:
5n - 3 < 3n + 3
Next, we can separate the n term from the constant term:
5n - 3n < 3 + 3
2n < 6
To solve for n, we divide both sides of the inequality by 2:
2n/2 < 6/2
n < 3
Therefore, the solution to the inequality is n < 3.
To represent this on a graph, we can draw an open circle at 3 on the number line, indicating that 3 is not included in the solution, and draw an arrow to the left, showing that the values of n which are less than 3 are part of the solution set.