Answer:
(-∞, 3] ∪ (3, ∞)
Step-by-step explanation:
Given compound inequality:
[tex]3x - 4 > 5\;\textsf{or}\;1 - 2x \geq 7[/tex]
To solve the compound equality, begin by solving each inequality separately.
Solve the first inequality:
[tex]3x-4 > 5 \\\\3x-4+4 > 5+4 \\\\3x > 9 \\\\x > \dfrac{9}{3} \\\\x > 3[/tex]
Solve the second inequality:
[tex]1-2x\geq 7 \\\\1-2x+2x\geq 7+2x \\\\1\geq 7+2x \\\\1-7\geq 7+2x-7 \\\\-6\geq 2x \\\\2x\leq -6 \\\\x\leq\dfrac{-6}{2}\\\\x\leq -3[/tex]
Therefore, the solutions to the individual inequalities are:
[tex]x > 3\\\\ x\leq-3[/tex]
Since these are "or" inequalities, we combine the solutions.
These are written with the symbol ∪ and represent the union of the solution sets, meaning the values that satisfy at least one of the inequalities.
Therefore, the solution to the compound inequality is:
[tex]\Large\boxed{\boxed{x\leq-3\;\textsf{or}\;x > 3}}[/tex]
In interval notation this is:
[tex]\Large\boxed{\boxed{(-\infty,-3]\cup(3,\infty)}}[/tex]