Question

solve the inequality. graph the solution on a number line and represent the solution in interval nota x + 7>4 select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the solution is x≥ - 3. (simplify your answer. type an inequality.) b. the solution is all real numbers. c. there is no solution.

Explanation:

Step1: Isolate the variable x

Subtract 7 from both sides of the inequality $x + 7>4$. We get $x+7 - 7>4 - 7$, which simplifies to $x>- 3$.

Step2: Analyze the solution

The solution of the inequality $x + 7>4$ is $x>-3$. The given option A ($x\geq - 3$) is incorrect as the original inequality is a strict - inequality. The solution is not all real numbers (option B is incorrect) and there is a solution (so option C is incorrect).

Answer:

The solution of the inequality $x + 7>4$ is $x>-3$. In interval notation, it is $(-3,\infty)$. To graph it on a number line, draw an open circle at - 3 (because - 3 is not included in the solution) and draw an arrow to the right to represent all numbers greater than - 3. There is no correct option among A, B, and C as presented. The correct inequality for the solution is $x > - 3$.