Given Inequality:
\(2(2x + 3) - 10 < 6(x - 2)\)
Step 1: Expand both sides
Left-hand side:
\(2(2x + 3) - 10 = 4x + 6 - 10 = 4x - 4\)
Right-hand side:
\(6(x - 2) = 6x - 12\)
Step 2: Form the inequality
\(4x - 4 < 6x - 12\)
Step 3: Solve the inequality
Subtract 4x from both sides:
\(-4 < 2x - 12\)
Add 12 to both sides:
\(8 < 2x\)
Divide both sides by 2:
\(x > 4\)
Graphical Representation on Number Line:
An open circle at 4 and the region to the right of 4 is shaded.
Final Answer:
The solution set is
{ x ∣ x > 4 }