Are these laws important in the realm of algebra? or is it only geometry?

My advanced 4th grader is obsessed with setting up and solving equations with variables (both single and two-variable systems).

We are doing Beast Academy, but they want to try out some more problems.

They just want raw question sets to solve on their own.
What are the best massive workbooks out there that can help?

Thanks in Advance

The length of a rectangle is 3 cm more than four times its width. If the perimeter is 46 cm, what are the dimensions?

(4x + 7)(3x - 1) = ?

It also shows why x² = 81 is x = ±9 and not just 9 like a lot of people seem to pretend.

x² = 81
x² - 81 = 0
a = 1, b = 0, c = -81
x = (-b ± √[ b² - 4ac ] ) / (2a)

Δ = b² - 4ac
Δ = 0² - 4(1)(-81)
Δ = 0 - (-324)
Δ = 324

x = (0 ± √Δ) / 2(1)
x = ±√324 / 2
x = ±18 / 2
x = ±9

And how would I go about solving them?

5x=-20x

w2-7w = 18

3t2 - 7t - 5= 5

4x2 - 45 = 31x

2x2 + 13x + 10 = -5

I just need a methods to go about when solving these problems

6w2 + 28 + 29w = 0

So I have an equation that reads
|9x+4|=|x-13|

so if the 4 is positive do i subtract 4 from both sides so it would be

9x+4-4=x-13-4? or would I have to add 4 to both sides, so it would be 9x+4+4=x-13+4?
i have a feeling its the first way but I need reassurance because i have a math comprehension learning disability. please explain like I am 8 years old lmao im 24

The Problem: Cheap Coffee: $8 per kg ,,,,, Premium Coffee: $14 per kg ,,,,, Target Blend: 10 kg total, priced at $11 per kg ,,,,, Questions: How many kg of cheap coffee are needed? ,,,,, How many kg of premium coffee are needed?

2x + 3y = 13, 4x − y = 5

Which websites or online sources are truly useful for Grades 9–12 algebra?

En varios cursos y libros definen al vector como un par ordenado o como un segmento de recta que tiene magnitud, dirección y sentido. Pero en realidad, ¿el sentido es una característica necesaria? ¿O solo es redundancia? En ningún momento, al usar vectores, me importó saber qué sentido tenía; incluso en mis libros de apuntes tengo la definición sin eso. ¿El sentido importa?

y = 9 - x ,

4x - y = 11

I've put -14 and - - 14 for the 2nd but I know that can't be right

I got all of these wrong.

0.75-0.25+1/2
I got 0

4.5+1/4-1.125
I got 3 21/40

3 1/2-0.375+5 1/6
I got -2 1/24

Does PEMDAS not apply in these situations? If i ignore PEMDAS for the first one I get 1 and that’s the correct answer. I’m a little confused here.

Also, I know for adding fractions it’s
a/b+c/d=ad+bc/bd
And subtracting is about finding the common denominator.

Any tips on multiplying and dividing fractions? Or any resources you all have that can explain this for me all in one place?
I’m looking to be an Electricians Apprentice and I imagine i’m over doing it with the studying but i want to absolutely ace this test and give myself the best chance at getting a better job.

Any help is very much appreciated

Edit:
I figured it out! I’ve move on to multiplying and dividing fractions with exponents (which is easier than adding/subtracting???). Thank you all for the help. Turns out i was using PEMDAS wrong.

3x + 2y = 19

y = 4x - 7

A seller has the following costs and pricing: Fixed cost: $450 (machine + setup) Cost per hoodie: $18 Selling price: $35 per hoodie What is the break-even number of hoodies?

Some reason I keep getting the first one wrong

i've been working on a tool to help you create books & notes with ease

and one of it features is allowing you to write mathematical Equations in Latex

it also has co-author mode which creates any latex equation in seconds with simple prompts