Question

did you hear about...
solve each inequality or problem. write the word under the correct solution in the box containing the exercise number.
answers 1 - 7
1 (7x + 2>4x + 15)
2 (10 - 3xgeq5x + 26)
3 (9x + 40leq15 - x)
4 (3(x - 7)>18)
5 (75<-5(4x + 1))
6 (6(2x - 9)geq4 + 11x)
7 (8 - 3(4x - 1)leq - 49)
answers 8 - 15
8 (2(t + 5)>4t - 7(t + 3))
9 (-4(3t - 9)geq8(-8 - t))
10 (14-(9t - 2)<-t + 30)
11 (45>12t + 3(t - 8)-6)
12 (5(8 - 2t)leq2 + 16(4 + t))
13 (7(5t - 4)-(2 + 15t)<60)
14 (9(9t - 4)geq12(12t - 3))
15 suppose you write a book. the printer charges $4 per book to print it, and you spend $3500 on advertising. you sell the book for $15 a copy. how many copies must you sell so that your income from sales is greater than your total cost?
answers 1 - 7:
(xgeq44) often
(xleq - 2\frac{1}{2}) and
(x>15) her
(x>4\frac{1}{3}) the
(x<-7) monkeys
(x>13) guy
(xgeq58) met
(xgeq8) when
(xleq - 2) girl
(xgeq5) in
(xleq - 4\frac{2}{3}) friends
(x<-4) who
answers 8 - 15:
(t>-1\frac{3}{4}) door
(t<8) spinning
(tleq0) around
(geq308) circles
(tleq25) revolving
(tgeq - 1) started
(tleq3\frac{1}{3}) in
(geq319) together
(t<5) and
(t>-6\frac{1}{5}) a
(t<4\frac{1}{2}) going
(tgeq - 3) dizzy
punchline • algebra • book a

Explanation:

Step1: Solve inequality 1

Subtract \(4x\) from both sides of \(7x + 2>4x + 15\): \(7x-4x+2>4x - 4x+15\), which simplifies to \(3x+2>15\). Then subtract 2 from both sides: \(3x+2 - 2>15 - 2\), getting \(3x>13\). Divide both sides by 3: \(x>\frac{13}{3}=4\frac{1}{3}\).

Step2: Solve inequality 2

First, expand both sides of \(10 - 3x\geq5x + 26\). Then add \(3x\) to both sides: \(10-3x + 3x\geq5x+3x + 26\), which gives \(10\geq8x + 26\). Subtract 26 from both sides: \(10-26\geq8x+26 - 26\), so \(- 16\geq8x\). Divide both sides by 8: \(x\leq - 2\).

Step3: Solve inequality 3

Add \(x\) to both sides of \(9x + 40\leq15 - x\): \(9x+x+40\leq15 - x+x\), getting \(10x+40\leq15\). Subtract 40 from both sides: \(10x+40 - 40\leq15 - 40\), so \(10x\leq - 25\). Divide both sides by 10: \(x\leq-\frac{25}{10}=-2\frac{1}{2}\).

Step4: Solve inequality 4

Expand the left - hand side of \(3(x - 7)>18\) to get \(3x-21>18\). Add 21 to both sides: \(3x-21 + 21>18 + 21\), so \(3x>39\). Divide both sides by 3: \(x>13\).

Step5: Solve inequality 5

Expand the right - hand side of \(75<-5(4x + 1)\) to get \(75<-20x - 5\). Add 5 to both sides: \(75 + 5<-20x-5 + 5\), so \(80<-20x\). Divide both sides by \(-20\) and reverse the inequality sign: \(x<-4\).

Step6: Solve inequality 6

Expand the left - hand side of \(6(2x - 9)\geq4 + 11x\) to get \(12x-54\geq4 + 11x\). Subtract \(11x\) from both sides: \(12x-11x-54\geq4+11x - 11x\), so \(x-54\geq4\). Add 54 to both sides: \(x\geq58\).

Step7: Solve inequality 7

Expand the left - hand side of \(8 - 3(4x - 1)\leq - 49\) to get \(8-12x + 3\leq - 49\), which simplifies to \(11-12x\leq - 49\). Subtract 11 from both sides: \(11-11-12x\leq - 49 - 11\), so \(-12x\leq - 60\). Divide both sides by \(-12\) and reverse the inequality sign: \(x\geq5\).

Step8: Solve inequality 8

Expand both sides of \(2(t + 5)>4t-7(t + 3)\): \(2t + 10>4t-7t-21\). Combine like terms: \(2t + 10>-3t-21\). Add \(3t\) to both sides: \(2t+3t + 10>-3t+3t-21\), so \(5t + 10>-21\). Subtract 10 from both sides: \(5t+10 - 10>-21 - 10\), so \(5t>-31\). Divide both sides by 5: \(t>-\frac{31}{5}=-6\frac{1}{5}\).

Step9: Solve inequality 9

Expand both sides of \(-4(3t - 9)\geq8(-8 - t)\): \(-12t + 36\geq - 64-8t\). Add \(12t\) to both sides: \(-12t+12t + 36\geq - 64-8t+12t\), so \(36\geq - 64 + 4t\). Add 64 to both sides: \(36 + 64\geq - 64+64 + 4t\), so \(100\geq4t\). Divide both sides by 4: \(t\leq25\).

Step10: Solve inequality 10

Expand the left - hand side of \(14-(9t - 2)<-t + 30\) to get \(14-9t + 2<-t + 30\), which simplifies to \(16-9t<-t + 30\). Add \(9t\) to both sides: \(16-9t+9t<-t+9t + 30\), so \(16<8t + 30\). Subtract 30 from both sides: \(16-30<8t+30 - 30\), so \(-14<8t\). Divide both sides by 8: \(t>-\frac{7}{4}=-1\frac{3}{4}\).

Step11: Solve inequality 11

Expand the right - hand side of \(45>12t+3(t - 8)-6\) to get \(45>12t+3t-24 - 6\). Combine like terms: \(45>15t-30\). Add 30 to both sides: \(45 + 30>15t-30 + 30\), so \(75>15t\). Divide both sides by 15: \(t<5\).

Step12: Solve inequality 12

Expand both sides of \(5(8 - 2t)\leq2 + 16(4 + t)\): \(40-10t\leq2 + 64+16t\). Combine like terms: \(40-10t\leq66 + 16t\). Add \(10t\) to both sides: \(40-10t+10t\leq66+16t + 10t\), so \(40\leq66 + 26t\). Subtract 66 from both sides: \(40-66\leq66-66 + 26t\), so \(-26\leq26t\). Divide both sides by 26: \(t\geq - 1\).

Step13: Solve inequality 13

Expand the left - hand side of \(7(5t - 4)-(2 + 15t)<60\) to get \(35t-28-2 - 15t<60\). Combine like terms: \(20t-30<60\). Add 30 to both sides: \(20t-30 + 30<60 + 30\), so \(20t<90\). Divide both sides by 20: \(t<\frac{9}{2}=4\frac{1}{2}\).

Step14: Solve inequality 14

Expand both sides of \(9(9t - 4)\geq12(12t - 3)\): \(81t-36\geq144t-36\). Subtract \(81t\) from both sides: \(81t-81t-36\geq144t-81t-36\), so \(-36\geq63t-36\). Add 36 to both sides: \(-36 + 36\geq63t-36 + 36\), so \(0\geq63t\). Divide both sides by 63: \(t\leq0\).

Step15: Solve problem 15

Let the number of copies be \(x\). The cost function \(C = 4x+3500\), and the income function \(I = 15x\). We want \(I>C\), so \(15x>4x + 3500\). Subtract \(4x\) from both sides: \(15x-4x>4x-4x + 3500\), so \(11x>3500\). Divide both sides by 11: \(x>\frac{3500}{11}\approx318.18\). Since \(x\) represents the number of copies, \(x\geq319\).

Answer:

1. THE
2. GIRL
3. AND
4. GUY
5. WHO
6. MET
7. IN
8. A
9. REVOLVING
10. DOOR
11. AND
12. STARTED
13. GOING
14. AROUND
15. TOGETHER