Solve the following inequality for x ∈ ℝ and show your solution on the numberline below: $2(3 - x) < 8$ Solve for x: $2^{2x-1} = 64$. - Leaving Cert Mathematics - Question 6 - 2019

To solve the inequality $2(3 - x) < 8$, we can start by simplifying it:

1. Distribute:

   $6 - 2x < 8$

2. Subtract 6 from both sides:

   $-2x < 2$

3. Divide both sides by -2, remembering to reverse the inequality sign:

   $x > -1$

4. Show on the number line:

   • Mark an open circle at $-1$ to indicate that $-1$ is not included in the solution.
   • Shade the line to the right of $-1$, indicating that $x$ can take any value greater than $-1$.