Question

lesson extra practice: writing and graphing inequalities write the word sentence as an inequality. 1. a number x is at most 3. 2. a number y added to 2 is greater than 7. 3. a number c multiplied by 3 is less than -12. 4. a number m minus 1.5 is no less than 2. 5. your friend writes the word sentence as an inequality. is your friend correct? explain your reasoning. three times a number z is more than 18. 3z < 18 tell whether the given value is a solution of the inequality. 6. t - 3 ≥ 2; t = 10 7. 6w < -2; w = 1 8. p + 1.6 ≤ 4; p = 5 9. \\(\frac{1}{2}d > -3\\); d = 0 copyright © big ideas learning, llc. all rights reserved. practice workbook: lesson and standards

Explanation:

Problem 1:

Step1: Understand "at most"

"At most" means the number \( x \) is less than or equal to 3.

Step2: Write the inequality

Translate the word sentence to an inequality: \( x \leq 3 \).

Step1: Analyze "added to" and "greater than"

"A number \( y \) added to 2" is \( y + 2 \), and "greater than 7" means \( y + 2>7 \).

Step2: Form the inequality

Combine the parts: \( y + 2>7 \).

Step1: Interpret "multiplied by" and "less than"

"A number \( c \) multiplied by 3" is \( 3c \), "less than - 12" gives \( 3c<-12 \).

Step2: Write the inequality

The inequality is \( 3c<-12 \).

Answer:

\( x \leq 3 \)

Problem 2: