Question

did you hear about . . .
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 ???
solve each inequality or problem. write the word under the correct solution in the box containing the exercise number.
answers 1-7
x ≥ 44 often
x ≤ -2½ and
x > 15 her
x > 4⅓ the
x < -7 monkeys
x > 13 guy
x ≥ 58 met
x ≥ 8 when
x ≤ -2 girl
x ≥ 5 in
x ≤ -4⅔ friends
x < -4 who
1 7x + 2 > 4x + 15
2 10 - 3x ≥ 5x + 26
3 9x + 40 ≤ 15 - x
4 3(x - 7) > 18
5 75 < -5(4x + 1)
6 6(2x - 9) ≥ 4 + 11x
7 8 - 3(4x - 1) ≤ -49
answers 8-15
t > -1¾ door
t < 8 spinning
t ≤ 0 around
≥ 308 circles
t ≤ 25 revolving
t ≥ -1 started
t ≤ 3⅓ in
≥ 319 together
t < 5 and
t > -6⅕ a
t < 4½ going
t ≥ -3 dizzy
8 2(t + 5) > 4t - 7(t + 3)
9 -4(3t - 9) ≥ 8(-8 - t)
10 14 - (9t - 2) < -t + 30
11 45 > 12t + 3(t - 8) - 6
12 5(8 - 2t) ≤ 2 + 16(4 + t)
13 7(5t - 4) - (2 + 15t) < 60
14 9(9t - 4) ≥ 12(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?
inequalities solving inequalities with parentheses and/or the variable... punchline • algebra • book a

Explanation:

Problem 1: \( 7x + 2 > 4x + 15 \)

Step 1: Subtract \( 4x \) from both sides

To isolate the variable terms on one side, we subtract \( 4x \) from each side of the inequality. This gives us \( 7x - 4x + 2 > 4x - 4x + 15 \), which simplifies to \( 3x + 2 > 15 \).

Step 2: Subtract 2 from both sides

Next, we subtract 2 from both sides to get the term with \( x \) alone. So, \( 3x + 2 - 2 > 15 - 2 \), which simplifies to \( 3x > 13 \).

Step 3: Divide by 3

Finally, we divide both sides by 3 to solve for \( x \). \( \frac{3x}{3} > \frac{13}{3} \), which simplifies to \( x > 4\frac{1}{3} \).

Step 1: Add \( 3x \) to both sides

To get all \( x \)-terms on one side, we add \( 3x \) to both sides. This gives \( 10 - 3x + 3x \geq 5x + 3x + 26 \), simplifying to \( 10 \geq 8x + 26 \).

Step 2: Subtract 26 from both sides

Subtract 26 from both sides: \( 10 - 26 \geq 8x + 26 - 26 \), which simplifies to \( -16 \geq 8x \).

Step 3: Divide by 8

Divide both sides by 8: \( \frac{-16}{8} \geq \frac{8x}{8} \), so \( -2 \geq x \) or \( x \leq -2 \).

Step 1: Add \( x \) to both sides

Add \( x \) to both sides to get \( 9x + x + 40 \leq 15 - x + x \), simplifying to \( 10x + 40 \leq 15 \).

Step 2: Subtract 40 from both sides

Subtract 40: \( 10x + 40 - 40 \leq 15 - 40 \), so \( 10x \leq -25 \).

Step 3: Divide by 10

Divide by 10: \( \frac{10x}{10} \leq \frac{-25}{10} \), simplifying to \( x \leq -2\frac{1}{2} \).

Answer:

\( x > 4\frac{1}{3} \) (matches "THE")

Problem 2: \( 10 - 3x \geq 5x + 26 \)