Simplifying and Combining Like Terms - Examples, Exercises and Solutions

Let's combine all the x terms together:

$7x+4x+5x=11x+5x=16x$

The resulting equation is:

$16x=0$

Now let's divide both sides by 16:

$\frac{16x}{16}=\frac{0}{16}$

$x=\frac{0}{16}=0$

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:

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

$b=2$

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:

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

$x=-4$

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:

$x=3-5$

$x=-2$

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:

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

$-4=x$

We will move the elements with the X to the left side and the elements without the X to the right side, changing the plus and minus signs accordingly.

First, we move the minus X to the left section:

$-\frac{1}{2}+\frac{1}{3}x+x=\frac{1}{5}$

Now we move the minus 1/2 to the right section:

$\frac{1}{3}x+x=\frac{1}{5}+\frac{1}{2}$

We will find a common denominator for the fractions on the right side and reduce accordingly. Convert the mixed fraction on the left side into a simple fraction:

$1\frac{1}{3}x=\frac{2+5}{10}$

$\frac{4}{3}x=\frac{7}{10}$

Multiply by$\frac{3}{4}$ to reduce the left side:

$x=\frac{7}{10}\times\frac{3}{4}=\frac{7\times3}{10\times4}=\frac{21}{40}$

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:

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

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

• Move similar terms to one side.

• Create common denominators using the least common multiple of the different fractions.

• Reduction of fractions.

First, we'll open the parentheses by multiplying each term by 4:

$4\times\frac{b}{2}+4\times b-\frac{1}{3}=6b$

Let's solve the multiplication exercise $4\times\frac{b}{2}=\frac{4b}{2}=2b$

Now the equation is:

$2b+4b-\frac{1}{3}=6b$

We'll combine the left side between the two b terms and get:

$6b-\frac{1}{3}=6b$

We'll reduce both sides by 6b and get:

$-\frac{1}{3}=0$

Since the result obtained is impossible, the exercise has no solution.