What is the solution set off 2x + 3 > 7 and 2x > 8

Answer 1

To solve the inequalities \(2x + 3 > 7\) and \(2x > 8\), we'll solve each inequality separately and then find the intersection of the solution sets.

1. Solving the first inequality: \[ 2x + 3 > 7 \] Subtract 3 from both sides: \[ 2x > 4 \] Now, divide both sides by 2: \[ x > 2 \]

2. Solving the second inequality: \[ 2x > 8 \] Divide both sides by 2: \[ x > 4 \]

Now we have two inequalities:

• From the first inequality: \(x > 2\)
• From the second inequality: \(x > 4\)

The more restrictive condition is \(x > 4\).

Solution set: The solution set is \(x > 4\). In interval notation, this can be written as \((4, \infty)\).