3x - 2 = 7 and 4x + 5 < 21

Answer 1

Let's solve each equation and inequality step by step.

1. For the equation \(3x - 2 = 7\):

   \[ 3x - 2 = 7 \]

   Add 2 to both sides:

   \[ 3x = 7 + 2 \] \[ 3x = 9 \]

   Now, divide both sides by 3:

   \[ x = \frac{9}{3} \] \[ x = 3 \]

2. For the inequality \(4x + 5 < 21\):

   \[ 4x + 5 < 21 \]

   Subtract 5 from both sides:

   \[ 4x < 21 - 5 \] \[ 4x < 16 \]

   Now, divide both sides by 4:

   \[ x < \frac{16}{4} \] \[ x < 4 \]

Summary of Solutions:

• The solution to the equation \(3x - 2 = 7\) is \(x = 3\).
• The solution to the inequality \(4x + 5 < 21\) is \(x < 4\).

The value \(x = 3\) satisfies the inequality \(x < 4\).