Question

solve the inequality. graph the solution on a number line and represent the solution in interval notation when possible. 2.1x + 18.6>46.5 - 7.2x
select the correct choice below and, if necessary, fill in the answer box to complete your choice
a. the solution is x>3 (type an inequality. simplify your answer.)
b. the solution is all real numbers
c. there is no solution
choose the correct graph of the solution set

Explanation:

Step1: Combine like - terms

Add \(7.2x\) to both sides of the inequality \(2.1x + 18.6>46.5−7.2x\):
\(2.1x+7.2x + 18.6>46.5−7.2x+7.2x\)
\(9.3x + 18.6>46.5\)

Step2: Isolate the variable term

Subtract \(18.6\) from both sides:
\(9.3x+18.6 - 18.6>46.5 - 18.6\)
\(9.3x>27.9\)

Step3: Solve for \(x\)

Divide both sides by \(9.3\):
\(x>\frac{27.9}{9.3}\)
\(x > 3\)

The graph of \(x>3\) on a number - line has an open circle at \(x = 3\) and a ray pointing to the right.

Answer:

A. The solution is \(x>3\)
C. (The graph with an open circle at \(3\) and a ray pointing to the right)