Simplifying and Combining Like Terms: Equations with variables on both sides

We will move terms so that on the left side of the equation, minus b remains

And to the right side, we will move 8 and make sure to keep the plus and minus signs accordingly:

$-b=6-8$

We will subtract accordingly:

$-b=-2$

We will divide both sides by minus 1 and be careful with the plus and minus signs when dividing by a negative:

$\frac{-b}{-1}=\frac{-2}{-1}$

$b=2$

We will rearrange the equation so that x remains on the left side and we will move similar elements to the right side.

Remember that when we move a positive number, it will become a negative number, so we will get:

$x=3-5$

$x=-2$

First, we divide both sections by 8:

$\frac{8(-2-x)}{8}=\frac{16}{8}$

Keep in mind that the 8 in the fraction of the left section is reduced, so the equation we get is:

$-2-x=2$

We move the minus 2 to the right section and maintain the plus and minus signs accordingly:

$-x=2+2$

$-x=4$

We divide both sides by minus 1 and maintain the plus and minus signs accordingly when we divide:

$\frac{-x}{-1}=\frac{4}{-1}$

$x=-4$

To solve the equation, we will move similar elements to one side.

On the right side, we place the elements with X, while in the left side we place the elements without X.

Remember that when we move sides, the plus and minus signs change accordingly, so we get:

$-9-3=2x+x$

We calculate both sides:$-12=3x$

Finally, divide both sides by 3:

$-\frac{12}{3}=\frac{3x}{3}$

$-4=x$

To solve this exercise, we first need to identify that we have an equation with an unknown,

To solve such equations, the first step will be to arrange the equation so that on one side we have the numbers and on the other side the unknowns.

$2X+7-5X-12=-8X+3$

First, we'll move all unknowns to one side.
It's important to remember that when moving terms, the sign of the number changes (from negative to positive or vice versa).

$2X+7-5X-12+8X=3$

Now we'll do the same thing with the regular numbers.

$2X-5X+8X=3-7+12$

In the next step, we'll calculate the numbers according to the addition and subtraction signs.

$2X-5X=-3X$
$-3X+8X=5X$

$3-7=-4$$$
$-4+12=8$

$5X=8$

At this stage, we want to get to a state where we have only one $X$, not $5X$,
so we'll divide both sides of the equation by the coefficient of the unknown (in this case - 5).

$X={8\over5}$

First, we will expand the parentheses on both sides:

$-3x-3+5x-4=-3+5x-5$

Enter the like terms in both sections. Let's start with the left section:

$-3x+5x=2x$

$-3-4=-7$

Calculate the like terms on the right side:

$-3-5=-8$

Now, we obtain the equation:

$2x-7=-8+5x$

To the right side we will move the members without the X, while to the left side we move those with the X, keeping the plus and minus signs as appropriate:

$2x-5x=-8+7$

$-3x=-1$

Finally, we divide both sides by -3:

$\frac{-1}{-3}=\frac{-3x}{-3}$

$\frac{1}{3}=x$

First, we will expand the parentheses on both sides by multiplying their contents by the number outside:

$-8+x-3\times x+(-3)\times(-2)=5\times2+5\times x-4+3x$

$-8+x-3x+6=10+5x-4+3x$

Now we collect like terms on both sides:

$-2-2x=6+8x$

We move 8x to the left and -2 to the right side, remembering to leave the plus and minus signs unchanged accordingly:

$-2x-8x=6+2$

We add the terms together:

$-10x=8$

Finally, we divide both sides by negative 10:

$\frac{-10x}{-10}=\frac{8}{-10}$

$x=-\frac{8}{10}$