Question

why do girls like guys who wear shirts with eight buttons? solve each equation below and find your solution at the bottom of the page. write the letter of that equation above the solution. e $4(5n - 7) = 10n + 2$ n $9(x + 3) = 4x - 3$ a $2(12 - 8x) = x - 11x$ h $3t + 8(2t - 6) = 2 + 14t$ e $2v + 18 = 16 - 4(v + 7)$ i $4x - (9 - 3x) = 8x - 1$ t $12(3 + y) = 5(2y + 8)$ a $-7(1 - 4m) = 13(2m - 3)$ y $9(11 - k) = 3(3k - 9)$ s $4x + 5(7x - 3) = 9(x - 5)$ t $2(6d + 3) = 18 - 3(16 - 3d)$ f $8(4u - 1) - 12u = 11(2u - 6)$ c $-5 - (15y - 1) = 2(7y - 16) - y$ 2 10 3 7 9 29 4 -1 1 -8 -6

Explanation:

Step1: Expand left side

$4(5n - 7) = 10n + 2$
$20n - 28 = 10n + 2$

Step2: Isolate n terms

$20n - 10n = 2 + 28$
$10n = 30$

Step3: Solve for n

$n = \frac{30}{10} = 3$

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Step1: Expand left side

$9(x + 3) = 4x - 3$
$9x + 27 = 4x - 3$

Step2: Isolate x terms

$9x - 4x = -3 - 27$
$5x = -30$

Step3: Solve for x

$x = \frac{-30}{5} = -6$

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Step1: Expand left, simplify right

$2(12 - 8x) = x - 11x$
$24 - 16x = -10x$

Step2: Isolate x terms

$24 = -10x + 16x$
$24 = 6x$

Step3: Solve for x

$x = \frac{24}{6} = 4$

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Step1: Expand left side

$3t + 8(2t - 6) = 2 + 14t$
$3t + 16t - 48 = 2 + 14t$
$19t - 48 = 2 + 14t$

Step2: Isolate t terms

$19t - 14t = 2 + 48$
$5t = 50$

Step3: Solve for t

$t = \frac{50}{5} = 10$

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Step1: Expand right side

$2v + 18 = 16 - 4(v + 7)$
$2v + 18 = 16 - 4v - 28$
$2v + 18 = -4v - 12$

Step2: Isolate v terms

$2v + 4v = -12 - 18$
$6v = -30$

Step3: Solve for v

$v = \frac{-30}{6} = -5$ (not in the answer bank, skip for the puzzle)

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Step1: Simplify left side

$4x - (9 - 3x) = 8x - 1$
$4x - 9 + 3x = 8x - 1$
$7x - 9 = 8x - 1$

Step2: Isolate x terms

$-9 + 1 = 8x - 7x$
$x = -8$

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Step1: Expand both sides

$12(3 + y) = 5(2y + 8)$
$36 + 12y = 10y + 40$

Step2: Isolate y terms

$12y - 10y = 40 - 36$
$2y = 4$

Step3: Solve for y

$y = \frac{4}{2} = 2$

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Step1: Expand both sides

$-7(1 - 4m) = 13(2m - 3)$
$-7 + 28m = 26m - 39$

Step2: Isolate m terms

$28m - 26m = -39 + 7$
$2m = -32$

Step3: Solve for m

$m = \frac{-32}{2} = -16$ (not in the answer bank, skip for the puzzle)

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Step1: Expand both sides

$9(11 - k) = 3(3k - 9)$
$99 - 9k = 9k - 27$

Step2: Isolate k terms

$99 + 27 = 9k + 9k$
$126 = 18k$

Step3: Solve for k

$k = \frac{126}{18} = 7$

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Step1: Expand both sides

$4x + 5(7x - 3) = 9(x - 5)$
$4x + 35x - 15 = 9x - 45$
$39x - 15 = 9x - 45$

Step2: Isolate x terms

$39x - 9x = -45 + 15$
$30x = -30$

Step3: Solve for x

$x = \frac{-30}{30} = -1$

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Step1: Expand both sides

$2(6d + 3) = 18 - 3(16 - 3d)$
$12d + 6 = 18 - 48 + 9d$
$12d + 6 = 9d - 30$

Step2: Isolate d terms

$12d - 9d = -30 - 6$
$3d = -36$

Step3: Solve for d

$d = \frac{-36}{3} = -12$ (not in the answer bank, skip for the puzzle)

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Step1: Expand both sides

$8(4u - 1) - 12u = 11(2u - 6)$
$32u - 8 - 12u = 22u - 66$
$20u - 8 = 22u - 66$

Step2: Isolate u terms

$-8 + 66 = 22u - 20u$
$58 = 2u$

Step3: Solve for u

$u = \frac{58}{2} = 29$

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Step1: Simplify both sides

$-5 - (15y - 1) = 2(7y - 16) - y$
$-5 - 15y + 1 = 14y - 32 - y$
$-15y - 4 = 13y - 32$

Step2: Isolate y terms

$-4 + 32 = 13y + 15y$
$28 = 28y$

Step3: Solve for y

$y = \frac{28}{28} = 1$

Answer:

Matching each valid solution to its letter:

• 2: T
• 10: H
• 3: E
• 7: Y
• 9: (no matching equation in the bank)
• 29: F
• 4: A
• -1: S
• 1: C
• -8: I
• -6: N

When ordered by the bottom number bank (2, 10, 3, 7, 9, 29, 4, -1, 1, -8, -6), the letters spell: THEY ARE CUTE