using the properties of inquality, justify both steps in solving the inequality 2/5m - 7 <_ 17

Answer 1

Step 1: Isolate the variable term

To solve the inequality, the first step is to isolate the variable term on one side of the inequality. In this case, that means getting rid of the -7 on the left side. We can do this by adding 7 to both sides of the inequality:

(2/5)m - 7 + 7 ≤ 17 + 7

Simplifying, we get:

(2/5)m ≤ 24

Step 2: Multiply both sides by the reciprocal

The second step is to multiply both sides of the inequality by the reciprocal of the fraction coefficient (2/5). In this case, the reciprocal is 5/2. By multiplying both sides by 5/2, we can eliminate the fraction:

(5/2)(2/5)m ≤ (5/2)(24)

Simplifying, we get:

(1)m ≤ 60/2
m ≤ 30

So, the solution to the inequality is m ≤ 30.

Answer 2

rewrite the equation 4x/3x-12 + 3 = 10 in two equations joined by " and."

Answer 3

Sure! Here are the two equations:

1. 4x/(3x - 12) + 3 = 10

Equation 1 can be rewritten as:

4x/(3x - 12) = 7

and

2. 4x/(3x - 12) + 3 = 10

Equation 2 can be rewritten as:

4x/(3x - 12) = 7