Question

in exercises 21 - 24, write the sentence as an inequality. then solve the inequality.

1. a number plus 8 is greater than 11.
2. a number minus 3 is at least - 5.
3. the difference of a number and 9 is fewer than 4.
4. six is less than or equal to the sum of a number and 15.
5. modeling with mathematics you are riding a train. your carry - on bag can weigh no more than 50 pounds. your bag weighs 38 pounds. (see example 3.)

a. write and solve an inequality that represents how much weight you can add to your bag.

Explanation:

Step1: Translate sentence 21 to inequality

Let the number be $x$. The inequality is $x + 8>11$.

Step2: Solve the inequality

Subtract 8 from both sides: $x+8 - 8>11 - 8$, so $x > 3$.

Step3: Translate sentence 22 to inequality

Let the number be $x$. The inequality is $x-3\geq - 5$.

Step4: Solve the inequality

Add 3 to both sides: $x-3 + 3\geq - 5+3$, so $x\geq - 2$.

Step5: Translate sentence 23 to inequality

Let the number be $x$. The inequality is $x - 9<4$.

Step6: Solve the inequality

Add 9 to both sides: $x-9 + 9<4 + 9$, so $x<13$.

Step7: Translate sentence 24 to inequality

Let the number be $x$. The inequality is $6\leq x + 15$.

Step8: Solve the inequality

Subtract 15 from both sides: $6-15\leq x+15 - 15$, so $-9\leq x$.

Step9: Translate 25a to inequality

Let the weight you can add be $w$. The inequality is $38 + w\leq50$.

Step10: Solve the inequality

Subtract 38 from both sides: $38 + w-38\leq50 - 38$, so $w\leq12$.

Answer:

1. Inequality: $x + 8>11$, Solution: $x>3$
2. Inequality: $x - 3\geq - 5$, Solution: $x\geq - 2$
3. Inequality: $x - 9<4$, Solution: $x<13$
4. Inequality: $6\leq x + 15$, Solution: $x\geq - 9$

25a. Inequality: $38 + w\leq50$, Solution: $w\leq12$