Question

solve the inequality and graph the solution. 2.5m - 1.5(2 - 3m) > 2(m + 1) plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it. (number line from -4 to 4 with marks at -4, -3, -2, -1, 0, 1, 2, 3, 4)

Explanation:

Step1: Expand the inequality

First, expand both sides of the inequality \(2.5m - 1.5(2 - 3m) > 2(m + 1)\).
Using the distributive property \(a(b - c)=ab - ac\), we get:
\(2.5m - 3 + 4.5m > 2m + 2\)

Step2: Combine like terms

Combine the \(m\)-terms on the left side:
\((2.5m + 4.5m)- 3 > 2m + 2\)
\(7m - 3 > 2m + 2\)

Step3: Subtract \(2m\) from both sides

Subtract \(2m\) from each side to get the \(m\)-terms on one side:
\(7m - 2m - 3 > 2m - 2m + 2\)
\(5m - 3 > 2\)

Step4: Add 3 to both sides

Add 3 to both sides to isolate the term with \(m\):
\(5m - 3 + 3 > 2 + 3\)
\(5m > 5\)

Step5: Divide by 5

Divide both sides by 5 to solve for \(m\):
\(\frac{5m}{5} > \frac{5}{5}\)
\(m > 1\)

Answer:

The solution to the inequality is \(m > 1\). To graph this, we draw an open circle at \(m = 1\) (since the inequality is strict, \(m
eq1\)) and draw a ray to the right of \(1\) on the number line.