Question

solve the inequality. graph the solution on a number line and represent the solution in interval notation when possible. -x + 5 < 7

b. the solution is all real numbers.
c. there is no solution.
choose the correct graph of the inequality.

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution written in interval notation is
b. there is no solution. it is not possible to write interval notation.

Explanation:

Step1: Isolate the variable term

Subtract 5 from both sides of $-x + 5<7$. We get $-x+5 - 5<7 - 5$, which simplifies to $-x<2$.

Step2: Solve for x

Multiply both sides of $-x < 2$ by - 1. Remember to reverse the inequality sign when multiplying by a negative number. So we have $x>-2$.

Answer:

The solution written in interval notation is $(-2,\infty)$. The correct graph is the one with an open - circle at - 2 and an arrow pointing to the right, which is not fully specified in the given options but conceptually matches the description of the solution set for $x > - 2$.