Question

Solve and represent the solution on a number line: 10x=3/3.5, where x>4.2.

Answer 1

The solution to the equation
`\(10x = (3)/(3.5)\)` is
`\(x = (3)/(35)\)`, and when considering the constraint
`\(x > 4.2\)`, the valid solution on the number line is
`\(x > 4.2\)`.

Step-by-step explanation:

Solving the equation
`\(10x = (3)/(3.5)\)` involves isolating
`\(x\)` by dividing both sides by 10, resulting in
`\(x = (3)/(35)\)`. This is the solution to the equation.

To represent this solution on a number line with the additional constraint
`\(x > 4.2\)`, we mark the point
`\(x = (3)/(35)\)` on the number line and shade the region to the right of 4.2. The inequality
`\(x > 4.2\)` indicates that any value of
`\(x\)`greater than 4.2 is a valid solution.

The number line representation visually communicates that the solution to the given equation is
`\(x = (3)/(35)\)`, and it satisfies the condition
`\(x > 4.2\)`. This type of representation is helpful for understanding the range of valid solutions within a specified range or condition.