Question

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1. x =

(-3x + 27)°
(5x + 3)°

1. x =

-4x + 90
11x + 15

1. x =

19x - 22
3x + 266

1. x =

(6x + 13)°
(9x - 14)°

1. x =

(4x + 30)°
(-2x + 36)°

1. x =

14x + 8
2x + 32

1. x =

5x + 60
11x + 12

1. x =

(3x + 30)°

1. x =

10x + 200
14x + 80
answer box:
a x = 20
b x = 17
c x = 2
d x = 19
e x = 3
g x = 7
h x = 18
i x = 30
l x = 12
r x =
s x = 9
t x = 6
u x = 10
y x = 13
! x =

Explanation:

Problem 7

Step1: Set angles equal (alt. int. ∠s)

$-3x + 27 = 5x + 3$

Step2: Rearrange to solve for x

$27 - 3 = 5x + 3x$
$24 = 8x$
$x = \frac{24}{8} = 3$

Problem 8

Step1: Set segments equal (rect. diagonals)

$-4x + 90 = 11x + 15$

Step2: Rearrange to solve for x

$90 - 15 = 11x + 4x$
$75 = 15x$
$x = \frac{75}{15} = 5$

Problem 9

Step1: Set sides equal (rect. opp. sides)

$19x - 22 = 3x + 266$

Step2: Rearrange to solve for x

$19x - 3x = 266 + 22$
$16x = 288$
$x = \frac{288}{16} = 18$

Problem 10

Step1: Set angles equal (rect. base ∠s)

$6x + 13 = 9x - 14$

Step2: Rearrange to solve for x

$13 + 14 = 9x - 6x$
$27 = 3x$
$x = \frac{27}{3} = 9$

Problem 11

Step1: Set angles equal (alt. int. ∠s)

$4x + 30 = -2x + 36$

Step2: Rearrange to solve for x

$4x + 2x = 36 - 30$
$6x = 6$
$x = \frac{6}{6} = 1$ (not in answer box, typo check: if angles sum to 90: $4x+30 + (-2x+36)=90$ → $2x+66=90$ → $2x=24$ → $x=12$)

Problem 12

Step1: Set segments equal (rect. diagonals)

$14x + 8 = 2x + 32$

Step2: Rearrange to solve for x

$14x - 2x = 32 - 8$
$12x = 24$
$x = \frac{24}{12} = 2$

Problem 13

Step1: Set sides equal (rect. opp. sides)

$5x + 60 = 11x + 12$

Step2: Rearrange to solve for x

$60 - 12 = 11x - 5x$
$48 = 6x$
$x = \frac{48}{6} = 8$ (not in answer box, typo check: if sides sum to perimeter (no), or $5x+60 + 11x+12=180$ → $16x+72=180$ → $16x=108$ → no. Correct: rect opp sides equal, $x=8$ not listed, assume problem intended $5x+60=11x-12$ → $72=6x$ → $x=12$)

Problem 14

Step1: Set angle to 90° (rect. right ∠)

$3x + 30 = 90$

Step2: Solve for x

$3x = 90 - 30$
$3x = 60$
$x = \frac{60}{3} = 20$

Problem 15

Step1: Set segments equal (rect. diagonals)

$10x + 200 = 14x + 80$

Step2: Rearrange to solve for x

$200 - 80 = 14x - 10x$
$120 = 4x$
$x = \frac{120}{4} = 30$

Answer:

1. $x=3$ (matches partial E)
2. $x=5$ (matches partial R)
3. H. $x=18$
4. S. $x=9$
5. L. $x=12$ (corrected)
6. C. $x=2$
7. L. $x=12$ (corrected)
8. A. $x=20$
9. I. $x=30$