Question

solve the inequality 7n+1>169

Answer 1

And how would we graph this? Step by step

Answer 2

-3x+5 (less than or equal to) 23

Answer 3

To solve the inequality 7n + 1 > 169, we will isolate n on one side of the expression.

First, subtract 1 from both sides:
7n + 1 - 1 > 169 - 1
7n > 168

Now, divide both sides of the inequality by 7:
7n/7 > 168/7
n > 24

Thus, the solution to the inequality 7n + 1 > 169 is n > 24.

Answer 4

To graph the inequality n > 24, we will create an open circle at the point 24 on the number line and shade to the right.

Here are the steps:

1. Draw a number line and label it with appropriate values.
2. Locate the point 24 on the number line.
3. Place an open circle at the point 24 to represent that it is not included in the solution.
4. Shade to the right of the open circle to indicate all values greater than 24 satisfy the inequality n > 24.

The resulting graph would have an open circle at 24 on the number line, and a shaded region to the right of the open circle.

Answer 5

To graph the inequality -3x + 5 ≤ 23, we will first solve it and then plot the graph.

Step 1: Solve the inequality.

-3x + 5 ≤ 23

Subtract 5 from both sides:

-3x ≤ 18

Divide both sides by -3 (since we are dividing by a negative number, we need to reverse the inequality symbol):

x ≥ -6

Step 2: Plot the graph.

1. Draw a number line and label it with appropriate values.
2. Mark a filled circle at -6 to represent that it is included in the solution.
3. Shade to the right of the filled circle to indicate all values greater than or equal to -6 satisfy the inequality.
- Since the inequality is "x ≥ -6," we shade to the right of the filled circle.

The resulting graph would have a filled circle at -6 on the number line, and a shaded region to the right of the filled circle.