Question

Please help me out fast

Graph the solution to this inequality on the number line.


3/5z > 3/4

Answer 1

Solution of inequality
`\((3)/(5)z > (3)/(4)\) is \((5)/(4)`

Given inequality:
`\((3)/(5)z > (3)/(4)\)`

1. Isolate the variable z:

`\((3)/(5)z > (3)/(4)\)`

2. To get rid of the fraction
`\((3)/(5)\)` with z, multiply both sides by the reciprocal of
`\((3)/(5)\)`, which is
`\((5)/(3)\)`.

But when you multiply or divide both sides of an inequality by a negative number, remember to flip the inequality sign.

`\[(5)/(3) * (3)/(5)z > (5)/(3) * (3)/(4)\] \(z > (5)/(12) * 3\)`

3. Simplify and solve:

`\((5)/(3) * (3)/(5)z = z\), and \((5)/(12) * 3 = (15)/(12) = (5)/(4)\)`

Therefore, after simplifying and solving the inequality, we find that the solution is
`\(z > (5)/(4)\)`.

Answer 2

Described below.

Explanation:

To graph the solution to an inequality on the number line, we need to determine the values of the variable that satisfy the inequality and then plot those values on the number line. In the given inequality, 35z > 34, we can solve for z by dividing both sides of the inequality by 35 to get:

z > 34/35

This gives us the solution z > 0.96857. To graph this solution on the number line, we can plot a dot at the value 0.96857, which represents the smallest value of z that satisfies the inequality. We can then draw a line segment to the right of this point, indicating that all values of z greater than 0.96857 are also solutions of the inequality. This is shown in the following diagram:

[Insert diagram of number line with dot at 0.96857 and line segment to the right]

As the inequality is strict (i.e., it uses the ">" symbol rather than "≥"), the values of z that exactly equal 0.96857 are not considered to be solutions. Only values of z that are greater than 0.96857 are considered to be solutions of the inequality.