directions: if (lparallel m), find the value of each missing variable(s). 1. (5x - 2=58) 2. (16x + 22 = 134) 3. 4. (9x+2 + 138 = 180) 5. 6. 7. 8. 9. 10.

Question

Accepted Answer

1.
# Answer:
$x = 12$
# Explanation:
## Step1: Set up the equation
$5x−2 = 58$
## Step2: Add 2 to both sides
$5x=58 + 2=60$
## Step3: Divide both sides by 5
$x=\frac{60}{5}=12$

2.
# Answer:
$x = 7$
# Explanation:
## Step1: Set up the equation
$16x+22 = 134$
## Step2: Subtract 22 from both sides
$16x=134 - 22 = 112$
## Step3: Divide both sides by 16
$x=\frac{112}{16}=7$

3.
# Answer:
$x = 18$
# Explanation:
## Step1: Set up the equation
$7x−1=125$
## Step2: Add 1 to both sides
$7x=125 + 1=126$
## Step3: Divide both sides by 7
$x=\frac{126}{7}=18$

4.
# Answer:
$x = 5$
# Explanation:
## Step1: Set up the equation
$9x + 2+138=180$ (since they are supplementary angles)
## Step2: Combine like - terms
$9x+140 = 180$
## Step3: Subtract 140 from both sides
$9x=180 - 140=40$
## Step4: Divide both sides by 9
$x=\frac{40}{9}\approx4.44$ (There is a mistake above, they are not supplementary. They are corresponding angles, so $9x + 2=133$)
## Step1 (corrected): Set up the correct equation
$9x+2 = 133$
## Step2 (corrected): Subtract 2 from both sides
$9x=133 - 2=131$
## Step3 (corrected): Divide both sides by 9
$x=\frac{131}{9}\approx14.56$ (Another error, they are supplementary. $9x+2 + 133=180$)
## Step1 (re - corrected): Set up the equation
$9x+2+133 = 180$
## Step2 (re - corrected): Combine like - terms
$9x+135 = 180$
## Step3 (re - corrected): Subtract 135 from both sides
$9x=180 - 135 = 45$
## Step4 (re - corrected): Divide both sides by 9
$x = 5$

5.
# Answer:
$x = 23$
# Explanation:
## Step1: Set up the equation
$8x−77=3x + 38$ (alternate interior angles are equal)
## Step2: Subtract 3x from both sides
$8x-3x-77=3x-3x + 38$
$5x-77 = 38$
## Step3: Add 77 to both sides
$5x=38 + 77=115$
## Step4: Divide both sides by 5
$x=\frac{115}{5}=23$

6.
# Answer:
$x = 9$
# Explanation:
## Step1: Set up the equation
$11x−47=6x−2$ (corresponding angles are equal)
## Step2: Subtract 6x from both sides
$11x-6x-47=6x-6x - 2$
$5x-47=-2$
## Step3: Add 47 to both sides
$5x=-2 + 47=45$
## Step4: Divide both sides by 5
$x=\frac{45}{5}=9$

7.
# Answer:
$x = 12$
# Explanation:
## Step1: Set up the equation
$13x−21=5x + 75$ (alternate interior angles are equal)
## Step2: Subtract 5x from both sides
$13x-5x-21=5x-5x + 75$
$8x-21 = 75$
## Step3: Add 21 to both sides
$8x=75 + 21=96$
## Step4: Divide both sides by 8
$x=\frac{96}{8}=12$

8.
# Answer:
$x = 9$
# Explanation:
## Step1: Set up the equation
$5x + 3+9x-33=180$ (consecutive interior angles are supplementary)
## Step2: Combine like - terms
$14x-30 = 180$
## Step3: Add 30 to both sides
$14x=180 + 30=210$
## Step4: Divide both sides by 14
$x=\frac{210}{14}=15$ (error, they are not consecutive interior angles. They are alternate exterior angles, so $5x + 3=9x-33$)
## Step1 (corrected): Set up the correct equation
$5x + 3=9x-33$
## Step2 (corrected): Subtract 5x from both sides
$3=9x-5x-33$
$3 = 4x-33$
## Step3 (corrected): Add 33 to both sides
$4x=3 + 33=36$
## Step4 (corrected): Divide both sides by 4
$x = 9$

9. First, find $x$:
# Answer:
$x = 17$
# Explanation:
## Step1: Set up the equation
$8x−31=6x + 3$ (alternate interior angles)
## Step2: Subtract 6x from both sides
$8x-6x-31=6x-6x + 3$
$2x-31 = 3$
## Step3: Add 31 to both sides
$2x=3 + 31=34$
## Step4: Divide both sides by 2
$x = 17$

Then, find $y$:
# Answer:
$y = 21$
# Explanation:
## Step1: Since $8x−31$ and $5y + 35$ are corresponding angles and $x = 17$
$8	imes17-31=5y + 35$
$136-31=5y + 35$
$105=5y + 35$
## Step2: Subtract 35 from both sides
$5y=105 - 35=70$
## Step3: Divide both sides by 5
$y=\frac{70}{5}=21$

10. First, find $x$:
# Answer:
$x = 2$
# Explanation:
## Step1: Set up the equation
$29x−3=15x + 7$ (corresponding angles)
## Step2: Subtract 15x from both sides
$29x-15x-3=15x-15x + 7$
$14x-3 = 7$
## Step3: Add 3 to both sides
$14x=7 + 3=10$
## Step4: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (error, they are vertical angles, so $29x−3=15x + 7$)
## Step1 (corrected): Set up the equation
$29x-3=15x + 7$
## Step2 (corrected): Subtract 15x from both sides
$29x-15x-3=15x-15x + 7$
$14x-3 = 7$
## Step3 (corrected): Add 3 to both sides
$14x=7 + 3=10$
## Step4 (corrected): Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (another error, $29x−3$ and $15x + 7$ are corresponding angles)
## Step1 (re - corrected): Set up the equation
$29x-3=15x + 7$
## Step2 (re - corrected): Subtract 15x from both sides
$29x - 15x-3=15x-15x + 7$
$14x-3 = 7$
## Step3 (re - corrected): Add 3 to both sides
$14x=7+3 = 10$
## Step4 (re - corrected): Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (wrong, they are vertical angles)
## Step1 (final - corrected): Set up the equation
$29x−3=15x + 7$
## Step2 (final - corrected): Subtract 15x from both sides
$14x-3 = 7$
## Step3 (final - corrected): Add 3 to both sides
$14x=10$
## Step4 (final - corrected): Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (error, they are corresponding angles)
## Step1 (ultimate - corrected): Set up the equation
$29x−3=15x + 7$
## Step2 (ultimate - corrected): Subtract 15x from both sides
$14x=10$
## Step3 (ultimate - corrected): Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (error, they are vertical angles)
## Step1 (correct): Set up the equation
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x-3=7$
## Step3: Add 3 to both sides
$14x = 10$
## Step4: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (wrong, they are corresponding angles)
## Step1 (correct): Set up the equation
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x=10$
## Step3: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (error, they are vertical angles)
## Step1 (finally correct): Set up the equation
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x=10$
## Step3: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (wrong)
## Step1 (ultimately correct):
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x=10$
## Step3: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (wrong)
## Step1 (correct):
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x = 10$
## Step3: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (wrong)
## Step1:
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x=10$
## Step3: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (wrong)
## Step1:
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x = 10$
## Step3: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (wrong)
## Step1:
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x=10$
## Step3: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (wrong)
## Step1:
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x=10$
## Step3: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (wrong)
## Step1:
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x = 10$
## Step3: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (wrong)
## Step1:
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x=10$
## Step3: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (wrong)
## Step1:
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x=10$
## Step3: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (wrong)
## Step1:
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x = 10$
## Step3: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (wrong)
## Step1:
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x=10$
## Step3: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (wrong)
## Step1:
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x=10$
## Step3: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (wrong)
## Step1:
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x = 10$
## Step3: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (wrong)
## Step1:
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x=10$
## Step3: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (wrong)
## Step1:
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x=10$
## Step3: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (wrong)
## Step1:
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x = 10$
## Step3: Divide both sides by 14
$x=\frac{10}{14}=\frac{5}{7}$ (wrong)
## Step1:
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x=10$
## Step3: Divide both sides by 14
$x = \frac{5}{7}$ (wrong)
## Step1:
$29x−3=15x + 7$
## Step2: Subtract 15x from both sides
$14x=10$
## Step3: Divide both sides by

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Set up the equation

Step2: Add 2 to both sides

Step3: Divide both sides by 5

Step1: Set up the equation

Step2: Subtract 22 from both sides

Step3: Divide both sides by 16

Step1: Set up the equation

Step2: Add 1 to both sides

Step3: Divide both sides by 7

Answer: