Uploaded March 2025 | Updated September 2026, 1 week ago
This math tutorial solves 100 precalculus equations and inequalities in one take, with clear and detailed explanations every step of the way. Topics include exponential and logarithmic equations, trigonometric identities, polynomial and rational inequalities, absolute value equations, and more. It’s designed for students who want a thorough review of precalculus concepts at a steady, easy-to-follow pace—perfect for building confidence and preparing for more advanced math.
Get your "algebra" t-shirt 👉 amzn.to/3A8Ed4k
File: 👉 patreon.com/posts/124068787
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Big thanks to my Patrons for the full-marathon support!
Ben D, Grant S, Mark M, Phillippe S. Michael Z, Jan P. Devun C. Stefan C. Ethan BW Didion S. NN Minkyu Y Brandon F Levon M shortsleeve Jack P Gabriel G Yeeted C David H Mateo F Emma M Eden E Minicat Jose R Nicholas Fey Tyler B Lucas W Ahmet Ö An R Camila L Luupo Farrah Batman 1127 Mathguru Дмитрий П. Michelle L. Alin V. Archer. L Ali. Subotai B. Spencer A. Chris Jason B. Ou S. Nuddi M. Jackson M. Jordan T. Gregorio B. Omkar N. John D. Zero Jeffrey C J D
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Huge thanks to @Rafsanul-Haq for the timestamps!
0:00 Solving 100 equations in one take!
1:00 (Q1.) √x + √(x+1) = 5
2:41 (Q2.) 8²ˣ⁻³ = 16
4:09 (Q3.) x³ - 3x² - 4x + 12 = 0
6:08 (Q4.) sinx + 1 = 0
7:55 (Q5.) x² + 7x - 3 = 0
10:13 (Q6.) { x = (1/2)y - 3
{ 4x - 5y = -6
12:14 (Q7.) x/(x+3) + 5/(2x+6) = 3/4
15:27 (Q8.) log₃₆(3x+15) = 1/2
18:26 (Q9.) |3x+1 - 2| = 4
19:56 (Q10.) 2cosx = -√3
24:42 (Q11.)
27:40 (Q12.) { 3x + 2y = 11
{ 4x - 5y = 30
31:21 (Q13.) 3e²ˣ⁺¹ - 4 = 56
33:28 (Q14.) 4x²e⁻ˣ - 2e⁻ˣ' = 0
36:06 (Q15.)
41:23 (Q16.) sin(2x) = sinx
46:56 (Q17.) x⁴ - 5x² + 4 = 0
48:48 (Q18.) ln(5x - 4) = 3
50:05 (Q19.)
53:31 (Q20.) √(5x - 4) = 1 + √(3x + 1)
58:22 (Q21.) 2sin²x + sinx = 0
1:01:31 (Q22.) x³ - 6x² + 11x - 6 = 0
1:05:41 (Q23.) -(1/2 + 3x) - 4 + 5x = 6x - 7 - (8x + 9)
1:10:24 (Q24.) 6sin²x + cos(2x) = 5
1:13:26 (Q25.) 3|5x - 2| + 16 = 4
1:14:40 (Q26.) log₂(x) + log₂(x+1) = 5
1:17:06 (Q27.) 2x³ - x = 14
1:23:14 (Q28.)
1:30:27 (Q29.) √(3 + 4√x) = 5
1:31:30 (Q30.) 5 = (4x + 3)(2x - 1)
1:34:25 (Q31.) |x| + |2x + 1| = 3
1:40:30 (Q32.) x² + (x + 1)² + (x + 2)² = 3
1:43:38 (Q33.) (2x + 1)² - 7(2x + 1) + 10 = 0
1:46:00 (Q34.) 16³ˣ⁺⁵ = 8⁴ˣ⁻²⁷
1:48:00 (Q35.) x⁴ + x³ + x + 1 = 0
1:54:17 (Q36.)
2:03:01 (Q37.) log₂(x + 5) - log₂(4x + 1) = 3
2:07:56 (Q38.) tan(3x) = 1
2:11:28 (Q39.) x³ + 3x² - 4x = 0
2:12:19 (Q40.) { x + y = 1500
{ 0.08x + 0.04y = 95
2:14:52 (Q41.)
2:17:40 (Q42.) 1/ln(x + 3) = 2
Accidentally skipped (Q43.) x³ - 5x + 4 = 0
2:19:02 (Q44.) |3x + 5| - 6 ≥ 14
2:21:04 (Q45.) 2ˣ + 2ˣ⁺¹ = 5
2:23:00 (Q46.) √3 sin x + cos x = 0
2:28:16 (Q47.)
2:30:04 (Q48.) log₆₄(5x - 1) = 2/3
2:31:36 (Q49.) log₂ x + log₂(x + 6) = 4
2:34:50 (Q50.) -12x + 3(4 + 5x) = 6(7/8 - x) + 9
2:39:31 (Q51.) cos(3x + π) = 0
2:41:31 (Q52.) (x + 1)/(x + 2) + (x + 3)/(x + 4) = 2
2:45:19 (Q53.)
2:51:07 (Q54.) 7³√(2x + 5) + 5 = 19
2:52:29 (Q55.) e²ˣ + 2eˣ - 15 = 0
2:55:00 (Q56.) { 3x + 2y = 5
{ 2x + 3y = -10
2:56:42 (Q57.) |4x + 3| = 2x
2:58:36 (Q58.) 5ˣ = 3ˣ⁺²
3:01:25 (Q59.) √3 sin x - cos x = 2
3:06:30 (Q60.) 16/x - 18/(x-1) + 2 = 0
3:08:56 (Q61.) (3x+1)² = 9
3:11:21 (Q62.) (3x+1)² = 9x
3:14:53 (Q63.)
3:19:00 (Q64.) 2cos²x - 7cos x + 3 = 0
3:22:45 (Q65.) 2x/(x-2) - (x-2)/(x-1) = (5x-6)/(x²-3x+2)
3:26:06 (Q66.) √(4x+1) + √(3x-2) = 1
3:31:12 (Q67.) 54/(1 + 3⁻ˣ) = 2
3:32:36 (Q68.) x⁴ - 8x² + 8 = 0
3:37:08 (Q69.) x³ = 64x
3:38:09 (Q70.) x³ = 64
3:41:20 (Q71.) 3csc²x - 4 = 0
3:46:37 (Q72.) |3x - 2| = |5x - 14|
3:48:45 (Q73.) (x-3)/(x²-3x+2) + 2/(x-2) = 2
3:51:56 (Q74.)
3:53:46 (Q75.) √(4x+5) = √x + 2
3:57:00 (Q76.) log₄(3/(x+15)) = -2
3:58:27 (Q77.)
3:59:54 (Q78.) {9x - 2y = 15
{3x + 5y = 27/2
4:02:28 (Q79.) x/(2x+3) - (x+3)/(x+4) = 1
4:06:56 (Q80.) 12(3)⁴ˣ⁻⁵ = 6
4:08:54 (Q81.) 2x + 1 = √(10x + 5)
4:11:36 (Q82.) 2³ˣ⁺¹ = 5ˣ⁺²
4:14:22 (Q83.)
4:16:56 (Q84.) 2/(x²+3x-4) = 0
4:17:57 (Q85.) tan(2x) = √3
4:19:19 (Q86.) 5000/(1 + e⁻⁰°²ˣ) = 4300
4:21:40 (Q87.) (x-1)²/⁴ = 25
4:24:35 (Q88.)
4:27:07 (Q89.)
4:31:30 (Q90.) (√2)³ˣ⁺⁶ = 8ˣ⁻⁵
4:34:11 (Q91.) (1 - cos x) / (1 + cos x) = 3
4:36:22 (Q92.) √(13 - x²) - 2 / √(13 - x²) = 1
4:42:53 (Q93.) { x - y = 5
{ √x - √y = 1
4:47:02 (Q94.) 1/2 x + 3/4 (x + 5) = 6 + 7/8 (x - 9)
4:49:40 (Q95.) 2 cos² x = 1 + sin x
4:55:38 (Q96.)
4:59:37 (Q97.) sin x + tan x = 0
5:02:20 (Q98.) log₉ x + log₃ x = 1
5:06:13 (Q99.) (eˣ - e⁻ˣ) / 2 = 1
5:11:16 (Q100.) √(4x² - 4x) = x
5:12:52 (Q101.) 3 / (2x - 4) + 1 / (x² + 3x + 2) = 1 / (2x - 4) - 2 / (x² - 4)
This math tutorial solves 100 precalculus equations and inequalities in one take, with clear and detailed explanations every step of the way. Topics include exponential and logarithmic equations, trigonometric identities, polynomial and rational inequalities, absolute value equations, and more. It’s designed for students who want a thorough review of precalculus concepts at a steady, easy-to-follow pace—perfect for building confidence and preparing for more advanced math.
Get your "algebra" t-shirt 👉 amzn.to/3A8Ed4k
File: 👉 patreon.com/posts/124068787
----------------------------------------
Big thanks to my Patrons for the full-marathon support!
Ben D, Grant S, Mark M, Phillippe S. Michael Z, Jan P. Devun C. Stefan C. Ethan BW Didion S. NN Minkyu Y Brandon F Levon M shortsleeve Jack P Gabriel G Yeeted C David H Mateo F Emma M Eden E Minicat Jose R Nicholas Fey Tyler B Lucas W Ahmet Ö An R Camila L Luupo Farrah Batman 1127 Mathguru Дмитрий П. Michelle L. Alin V. Archer. L Ali. Subotai B. Spencer A. Chris Jason B. Ou S. Nuddi M. Jackson M. Jordan T. Gregorio B. Omkar N. John D. Zero Jeffrey C J D
---------------------------------------
Huge thanks to @Rafsanul-Haq for the timestamps!
0:00 Solving 100 equations in one take!
1:00 (Q1.) √x + √(x+1) = 5
2:41 (Q2.) 8²ˣ⁻³ = 16
4:09 (Q3.) x³ - 3x² - 4x + 12 = 0
6:08 (Q4.) sinx + 1 = 0
7:55 (Q5.) x² + 7x - 3 = 0
10:13 (Q6.) { x = (1/2)y - 3
{ 4x - 5y = -6
12:14 (Q7.) x/(x+3) + 5/(2x+6) = 3/4
15:27 (Q8.) log₃₆(3x+15) = 1/2
18:26 (Q9.) |3x+1 - 2| = 4
19:56 (Q10.) 2cosx = -√3
24:42 (Q11.)
27:40 (Q12.) { 3x + 2y = 11
{ 4x - 5y = 30
31:21 (Q13.) 3e²ˣ⁺¹ - 4 = 56
33:28 (Q14.) 4x²e⁻ˣ - 2e⁻ˣ' = 0
36:06 (Q15.)
41:23 (Q16.) sin(2x) = sinx
46:56 (Q17.) x⁴ - 5x² + 4 = 0
48:48 (Q18.) ln(5x - 4) = 3
50:05 (Q19.)
53:31 (Q20.) √(5x - 4) = 1 + √(3x + 1)
58:22 (Q21.) 2sin²x + sinx = 0
1:01:31 (Q22.) x³ - 6x² + 11x - 6 = 0
1:05:41 (Q23.) -(1/2 + 3x) - 4 + 5x = 6x - 7 - (8x + 9)
1:10:24 (Q24.) 6sin²x + cos(2x) = 5
1:13:26 (Q25.) 3|5x - 2| + 16 = 4
1:14:40 (Q26.) log₂(x) + log₂(x+1) = 5
1:17:06 (Q27.) 2x³ - x = 14
1:23:14 (Q28.)
1:30:27 (Q29.) √(3 + 4√x) = 5
1:31:30 (Q30.) 5 = (4x + 3)(2x - 1)
1:34:25 (Q31.) |x| + |2x + 1| = 3
1:40:30 (Q32.) x² + (x + 1)² + (x + 2)² = 3
1:43:38 (Q33.) (2x + 1)² - 7(2x + 1) + 10 = 0
1:46:00 (Q34.) 16³ˣ⁺⁵ = 8⁴ˣ⁻²⁷
1:48:00 (Q35.) x⁴ + x³ + x + 1 = 0
1:54:17 (Q36.)
2:03:01 (Q37.) log₂(x + 5) - log₂(4x + 1) = 3
2:07:56 (Q38.) tan(3x) = 1
2:11:28 (Q39.) x³ + 3x² - 4x = 0
2:12:19 (Q40.) { x + y = 1500
{ 0.08x + 0.04y = 95
2:14:52 (Q41.)
2:17:40 (Q42.) 1/ln(x + 3) = 2
Accidentally skipped (Q43.) x³ - 5x + 4 = 0
2:19:02 (Q44.) |3x + 5| - 6 ≥ 14
2:21:04 (Q45.) 2ˣ + 2ˣ⁺¹ = 5
2:23:00 (Q46.) √3 sin x + cos x = 0
2:28:16 (Q47.)
2:30:04 (Q48.) log₆₄(5x - 1) = 2/3
2:31:36 (Q49.) log₂ x + log₂(x + 6) = 4
2:34:50 (Q50.) -12x + 3(4 + 5x) = 6(7/8 - x) + 9
2:39:31 (Q51.) cos(3x + π) = 0
2:41:31 (Q52.) (x + 1)/(x + 2) + (x + 3)/(x + 4) = 2
2:45:19 (Q53.)
2:51:07 (Q54.) 7³√(2x + 5) + 5 = 19
2:52:29 (Q55.) e²ˣ + 2eˣ - 15 = 0
2:55:00 (Q56.) { 3x + 2y = 5
{ 2x + 3y = -10
2:56:42 (Q57.) |4x + 3| = 2x
2:58:36 (Q58.) 5ˣ = 3ˣ⁺²
3:01:25 (Q59.) √3 sin x - cos x = 2
3:06:30 (Q60.) 16/x - 18/(x-1) + 2 = 0
3:08:56 (Q61.) (3x+1)² = 9
3:11:21 (Q62.) (3x+1)² = 9x
3:14:53 (Q63.)
3:19:00 (Q64.) 2cos²x - 7cos x + 3 = 0
3:22:45 (Q65.) 2x/(x-2) - (x-2)/(x-1) = (5x-6)/(x²-3x+2)
3:26:06 (Q66.) √(4x+1) + √(3x-2) = 1
3:31:12 (Q67.) 54/(1 + 3⁻ˣ) = 2
3:32:36 (Q68.) x⁴ - 8x² + 8 = 0
3:37:08 (Q69.) x³ = 64x
3:38:09 (Q70.) x³ = 64
3:41:20 (Q71.) 3csc²x - 4 = 0
3:46:37 (Q72.) |3x - 2| = |5x - 14|
3:48:45 (Q73.) (x-3)/(x²-3x+2) + 2/(x-2) = 2
3:51:56 (Q74.)
3:53:46 (Q75.) √(4x+5) = √x + 2
3:57:00 (Q76.) log₄(3/(x+15)) = -2
3:58:27 (Q77.)
3:59:54 (Q78.) {9x - 2y = 15
{3x + 5y = 27/2
4:02:28 (Q79.) x/(2x+3) - (x+3)/(x+4) = 1
4:06:56 (Q80.) 12(3)⁴ˣ⁻⁵ = 6
4:08:54 (Q81.) 2x + 1 = √(10x + 5)
4:11:36 (Q82.) 2³ˣ⁺¹ = 5ˣ⁺²
4:14:22 (Q83.)
4:16:56 (Q84.) 2/(x²+3x-4) = 0
4:17:57 (Q85.) tan(2x) = √3
4:19:19 (Q86.) 5000/(1 + e⁻⁰°²ˣ) = 4300
4:21:40 (Q87.) (x-1)²/⁴ = 25
4:24:35 (Q88.)
4:27:07 (Q89.)
4:31:30 (Q90.) (√2)³ˣ⁺⁶ = 8ˣ⁻⁵
4:34:11 (Q91.) (1 - cos x) / (1 + cos x) = 3
4:36:22 (Q92.) √(13 - x²) - 2 / √(13 - x²) = 1
4:42:53 (Q93.) { x - y = 5
{ √x - √y = 1
4:47:02 (Q94.) 1/2 x + 3/4 (x + 5) = 6 + 7/8 (x - 9)
4:49:40 (Q95.) 2 cos² x = 1 + sin x
4:55:38 (Q96.)
4:59:37 (Q97.) sin x + tan x = 0
5:02:20 (Q98.) log₉ x + log₃ x = 1
5:06:13 (Q99.) (eˣ - e⁻ˣ) / 2 = 1
5:11:16 (Q100.) √(4x² - 4x) = x
5:12:52 (Q101.) 3 / (2x - 4) + 1 / (x² + 3x + 2) = 1 / (2x - 4) - 2 / (x² - 4)
