To translate the sentence "Twice the difference of a number and 4 is less than -25" into an inequality, we can follow these steps:
1. Identify the variable: Let [tex]\( c \)[/tex] represent the unknown number.
2. Translate the phrases into mathematical expressions:
- "The difference of a number and 4" translates to [tex]\( c - 4 \)[/tex].
- "Twice" translates to multiplying by 2.
- "Is less than" is represented by the inequality symbol [tex]\( < \)[/tex].
- The number -25 remains as is.
3. Form the inequality:
- Twice the difference of a number and 4 can be written as [tex]\( 2 \times (c - 4) \)[/tex].
- So, we have [tex]\( 2 \times (c - 4) < -25 \)[/tex].
4. Simplify the inequality:
- Distribute the 2: [tex]\( 2(c - 4) < -25 \)[/tex].
- This becomes [tex]\( 2c - 8 < -25 \)[/tex].
5. Solve the inequality:
- Add 8 to both sides to isolate the term with the variable: [tex]\( 2c - 8 + 8 < -25 + 8 \)[/tex].
- Simplify the inequality: [tex]\( 2c < -17 \)[/tex].
- Finally, divide both sides by 2: [tex]\( c < -8.5 \)[/tex].
So, the inequality that represents "Twice the difference of a number and 4 is less than -25" is [tex]\( c < -8.5 \)[/tex].
