Which option correctly describes the values that make the inequality 2m<14 true when written in set notation?
Option #1: {m:m<7}
Option #2: {7:7<m}
Option #3: {m<7:m}
Option #4: {m<7}
The correct option that describes the values that make the inequality 2m<14 true when written in set notation is Option #1: {m:m<7}.
The correct option is Option #1: {m:m<7}.
This option correctly describes the values that make the inequality 2m<14 true. The inequality states that 2m is less than 14, so to find the range of values for m, we solve the inequality as follows:
2m < 14
m < 7
This means that the values of m that make the inequality true are less than 7. Therefore, the correct set notation for these values is {m:m<7}.
The correct option that describes the values making the inequality 2m < 14 true when written in set notation is Option #1: {m: m<7}.
To understand why this option is correct, let's break down the inequality. The inequality is 2m < 14, which means "2m is less than 14." To solve this inequality, we need to isolate the variable (m) on one side of the inequality.
Dividing both sides of the inequality by 2, we have m < 7. This indicates that m should be less than 7 in order for the inequality to be true.
Now, let's examine Option #1: {m: m<7}. In set notation, the expression {m: m<7} means "the set of all values of m such that m is less than 7." This aligns with the solution to the inequality, where m should be less than 7. Therefore, Option #1 {m: m<7} correctly describes the values that make the inequality 2m < 14 true when written in set notation.