Questions: Translate the sentence into an inequality. Two times the sum of a number and 24 is at least 17. Use the variable c for the unknown number.

Solution Steps

To translate the given sentence into an inequality, follow these steps:

1. Identify the unknown number and represent it with the variable \( c \).
2. Recognize the phrase "the sum of a number and 24" which translates to \( c + 24 \).
3. Note that "two times" this sum means multiplying the sum by 2, resulting in \( 2(c + 24) \).
4. The phrase "is at least 17" translates to the inequality \( \geq 17 \).
5. Combine these parts to form the inequality \( 2(c + 24) \geq 17 \).

The given sentence is "Two times the sum of a number and 24 is at least 17." We need to translate this into a mathematical inequality.

1. Let the unknown number be \( c \).
2. The sum of the number and 24 is \( c + 24 \).
3. Two times this sum is \( 2(c + 24) \).
4. The phrase "is at least 17" translates to \( \geq 17 \).

Thus, the inequality is: \[ 2(c + 24) \geq 17 \]

Simplify the inequality by distributing the 2 and then isolating \( c \).

1. Distribute the 2: \[ 2c + 48 \geq 17 \]

2. Subtract 48 from both sides: \[ 2c \geq 17 - 48 \] \[ 2c \geq -31 \]

3. Divide both sides by 2: \[ c \geq -\frac{31}{2} \]

Final Answer