Question

Is the solution to the inequality x>4 or x<4?

a) x>4
b) x<4
c) x≥4
d) x≤4

Answer 1

The solution to the inequality
`\(x > 4\) or \(x < 4\)` is represented as
`\(\mathbf{(c) \ x \geq 4}\).`

The inequality
`\(x > 4\) or \(x < 4\)`is satisfied by values greater than or equal to 4. The inclusive representation
`\(x \geq 4\)` ensures that 4 is part of the solution set.

Step-by-step explanation:

The given inequality
`\(x > 4\) or \(x < 4\)`indicates that the solution set includes all real numbers greater than 4 or less than 4. The symbol
`\(\mathbf{or}\)`suggests that either condition can be satisfied for a valid solution. To represent this on the number line, we consider values greater than 4 (including 4) and values less than 4. Therefore, the solution set can be expressed as \(x \geq 4\) since it encompasses all values greater than or equal to 4. This is denoted by the symbol
`\(\geq\),` which includes the boundary value.

In mathematical terms, when
`\(x \geq 4\),` it means that
`\(x\)` can be 4 or any number greater than 4. The inclusion of the equality sign
`\(\geq\)` is crucial here, indicating that 4 is part of the solution set. If
`\(x > 4\)`was the correct representation without the equality sign, the value 4 would not be included in the solution set. Hence, to accurately capture all possible solutions, the correct representation is
`\(x \geq 4\),` making option
`\(\mathbf{(c)}\)` the final answer.