Which graph represents the solutions to this inequality: 5n−3<3(n+1)

Answer 1

To solve the inequality \( 5n - 3 < 3(n + 1) \), let's start by simplifying the right side:

1. Distribute the 3 on the right side: \[ 3(n + 1) = 3n + 3 \] So, the inequality becomes: \[ 5n - 3 < 3n + 3 \]

2. Next, let's isolate \( n \). First, subtract \( 3n \) from both sides: \[ 5n - 3n - 3 < 3 \] which simplifies to: \[ 2n - 3 < 3 \]

3. Now, add 3 to both sides: \[ 2n < 6 \]

4. Finally, divide both sides by 2: \[ n < 3 \]

This means the solutions to the inequality are all values of \( n \) that are less than 3.

To represent this graphically:

• A number line would show an open circle at 3 (indicating that 3 is not included) and a line extending to the left (indicating all values less than 3).

Make sure to look for this type of representation in the graphs available to you.

Answer 2

Graph the solutions for the inequality: −3x+1≤−47(2 points)
Responses

Answer 3

To solve the inequality \(-3x + 1 \leq -47\), follow these steps:

1. Subtract 1 from both sides: \[ -3x + 1 - 1 \leq -47 - 1 \] This simplifies to: \[ -3x \leq -48 \]

2. Divide both sides by -3: Remember that when you divide or multiply by a negative number, you must flip the inequality sign: \[ x \geq 16 \]

The solution to the inequality is \(x \geq 16\).

Graphical Representation:

On a number line, you would represent this as:

• A closed circle (or filled dot) at 16 (indicating that 16 is included in the solution).
• A line extending to the right from the closed circle (indicating all values greater than or equal to 16).

Make sure to look out for this representation when examining possible graph options.