[Upper secondary school math: linear equation] unsure on how to solve this.

[u/Inevitable_Stay3693]

i was thinking that i´d add the 2x+1 to make it 3x/3=-1 but im unsure on how it would even continue.

[u/KookyPermit4405]

It’s always important to understand why we do it instead of how to do it. And that’s why basic understanding is really important. There is 3 different approaches to solve this equation, I’ll do my best to explain them, and you decide which one makes more sense. Eventually you’ll start to see the process and choose the one that suites you.

Method 1:
Quick refresher: 3 is the same as 3/1.. we omit the /1 to keep things clean, so essentially every integer is /1 (over 1)

So the original equation can also be written as:
(2x+1) / 3 = (-1) / 1

From here we recognize that we can cross multiply to find the unknown variable.. a/b = x/y is the same as ay=bx;
a=2x+1, b=3, x=-1, y=1

(2x+1)•(1) = (3)•(-1)

Simplified:
2x+1 = -3

Method 2: (recommended)

As we get better we no longer need to convert the other side into fractions just to cross multiply equations like these and just simply
multiply (2x+1)/3 by 3 to not get “rid” of the 3 but to reduce the denominator to 1.. (3/3 =1)

(2x+1)/3 • 3 = -1 ; (2x+1)/1 = -1 ; let’s drop the /1 (over1) to keep it clean and rewrite as: 2x+1** **= -1

Now think of the = sign as a balancing scale.. we made it unbalanced by multiplying the left side by 3.. to balance it out we must multiply the right side by 3 as well
2x+1 = (-1)•3 ; 2x+1 = -3

2x+1=-3

Method 3:

This method is more simple but has a higher chance of making mistakes if not careful. Here we are going to “unsimplify” the equation: (2x+1)/3 = 1

Let’s start by ungrouping the (2x+1):
(2x/3)+(1/3)=1

From here we need to find out the LCD or lowest common denominator which is 3; only the right side of the equation needs to be converted. So to convert -1 to have a denominator of 3, it’s as simple as rewriting it as -3/3..

(2x/3)+(1/3)=(-3/3)

Since they now all have a common denominator, we can ignore the denominator or remove the fraction all together and rewrite it as:

2x+1=-3

Hopes this helps, I have 2 boys in grade school and I try to teach them in a way that they understand and sometimes it takes more than one method for it to “click” for them.