Question

where do young tigers swim? write the letter of each answer in the box containing the exercise number. solve the inequality. 1. 4x - 7 < 9 2. -11 > 10 - 7x 3. $\frac{x}{6}+5 > 8$ 4. $\frac{x}{2}+12 geq 14$ 5. 6x - 23 > 25 6. 6 - $\frac{x}{5} geq -2$ 7. 3 $geq -3(x - 13)$ 8. 16 - 4x > 9 - 5x 9. 2x + 7 $leq 2x + 8$ 10. -6(x - 1) < -14(x - 5) 11. 12x + 4x - 11 $geq 16x + 17$ 12. 3(1 - x) + 10x $leq 9(x - 2) + 7$ 13. the students in charge of the class booth at a carnival want to make a profit of at least $65 by selling items. they spent $55 for the materials to make the items. they will sell each item for $3. find the possible values of x, the number of items the students need to sell to reach their goal. 14. a triangle has a base of 14 centimeters and a height of (3x - 4) centimeters. the area of the triangle is greater than 56 centimeters. find the possible values of x. answers n. all real numbers k. x $geq 7$ p. x < 8 e. x > 3 o. x < 4 i. x > 8 o. x $geq 40$ y. x $leq -4$ t. x > 4 l. x > -7 t. no solution h. x $geq 12$ i. x $leq 40$ t. x > 18

Explanation:

Step1: Solve $4x - 7 < 9$

Add 7 to both sides: $4x<9 + 7$, so $4x<16$. Then divide both sides by 4, we get $x < 4$. The answer is O.

Step2: Solve $-11>10 - 7x$

Subtract 10 from both sides: $-11-10>-7x$, so $-21>-7x$. Divide both sides by - 7 and reverse the inequality sign, we have $x > 3$. The answer is E.

Step3: Solve $\frac{x}{6}+5>8$

Subtract 5 from both sides: $\frac{x}{6}>8 - 5$, so $\frac{x}{6}>3$. Multiply both sides by 6, we get $x>18$. The answer is T.

Step4: Solve $\frac{x}{2}+12\geq14$

Subtract 12 from both sides: $\frac{x}{2}\geq14 - 12$, so $\frac{x}{2}\geq2$. Multiply both sides by 2, we have $x\geq4$. There is no match in the given answers.

Step5: Solve $6x - 23>25$

Add 23 to both sides: $6x>25 + 23$, so $6x>48$. Divide both sides by 6, we get $x > 8$. The answer is I.

Step6: Solve $6-\frac{x}{5}\geq - 2$

Subtract 6 from both sides: $-\frac{x}{5}\geq-2 - 6$, so $-\frac{x}{5}\geq - 8$. Multiply both sides by - 5 and reverse the inequality sign, we have $x\leq40$. The answer is I.

Step7: Solve $3\geq - 3(x - 13)$

Divide both sides by - 3 and reverse the inequality sign: $-1\leq x - 13$. Add 13 to both sides, we get $x\geq12$. The answer is H.

Step8: Solve $16-4x>9 - 5x$

Add $5x$ to both sides: $16-4x + 5x>9$, so $16+x>9$. Subtract 16 from both sides, we have $x>-7$. The answer is L.

Step9: Solve $2x + 7\leq2x + 8$

Subtract $2x$ from both sides: $7\leq8$. This is true for all real - numbers. The answer is N.

Step10: Solve $-6(x - 1)<-14(x - 5)$

Expand both sides: $-6x+6<-14x + 70$. Add $14x$ to both sides: $-6x+14x+6<70$, so $8x+6<70$. Subtract 6 from both sides: $8x<64$. Divide both sides by 8, we get $x < 8$. The answer is R.

Step11: Solve $12x + 4x-11\geq16x + 17$

Combine like - terms: $16x-11\geq16x + 17$. Subtract $16x$ from both sides: $-11\geq17$, which is false. So there is no solution. The answer is T.

Step12: Solve $3(1 - x)+10x\leq9(x - 2)+7$

Expand both sides: $3-3x+10x\leq9x-18 + 7$. Combine like - terms: $3 + 7x\leq9x-11$. Subtract $7x$ from both sides: $3\leq2x-11$. Add 11 to both sides: $14\leq2x$. Divide both sides by 2, we get $x\geq7$. The answer is K.

Step13: Set up the inequality $3x-55\geq65$

Add 55 to both sides: $3x\geq65 + 55$, so $3x\geq120$. Divide both sides by 3, we have $x\geq40$. The answer is O.

Step14: Use the area formula of a triangle $A=\frac{1}{2}bh$. Here $A=\frac{1}{2}\times14\times(3x - 4)>56$

First simplify the left - hand side: $7(3x - 4)>56$. Expand: $21x-28>56$. Add 28 to both sides: $21x>56 + 28$, so $21x>84$. Divide both sides by 21, we get $x > 4$. The answer is T.

Answer:

1. O. $x < 4$
2. E. $x > 3$
3. T. $x>18$
4. No match
5. I. $x > 8$
6. I. $x\leq40$
7. H. $x\geq12$
8. L. $x>-7$
9. N. all real numbers
10. R. $x < 8$
11. T. no solution
12. K. $x\geq7$
13. O. $x\geq40$
14. T. $x > 4$