Solving Equations Using All Methods: Equations with variables on both sides

Question 1

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

Question 2

Find the value of the parameter X

$$ -3x+8-11=40x+5x+9 $$

Question 3

Solve for X:

$$ x+3-4x=5x+6-1-8x $$

Question 4

Find the value of the parameter X

$$ -31+48x+46=83x-85+15x $$

Question 5

Find the value of the parameter X

$$ -33x+45-58=38x+144-15 $$

Examples with solutions for Solving Equations Using All Methods: Equations with variables on both sides

Exercise #1

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

Video Solution

Step-by-Step Solution

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).

$X={8\over5}$

Answer

$x=\frac{8}{5}$

Exercise #2

Find the value of the parameter X

$-3x+8-11=40x+5x+9$

Video Solution

Answer

$-\frac{1}{4}$

Exercise #3

Solve for X:

$x+3-4x=5x+6-1-8x$

Video Solution

Answer

No solution

Exercise #4

Find the value of the parameter X

$-31+48x+46=83x-85+15x$

Video Solution

Answer

$2$

Exercise #5

Find the value of the parameter X

$-33x+45-58=38x+144-15$

Video Solution

Answer

$-2$

Question 1

Find the value of the parameter X

$$ 74-6x+3=8x+5x-18 $$

Question 2

Solve for X:

$$ -22x+35-4x=31-8+10x $$

Question 3

Solve for X:

$$ 36x-52+8x=19x+54-31 $$

Question 4

Solve for X:

$$ -45+3x+99=5x+11x+2 $$

Question 5

Solve for X:

$$ 54x-36x+34=39+5x-18 $$

Exercise #6

Find the value of the parameter X

$74-6x+3=8x+5x-18$

Video Solution

Answer

$5$

Exercise #7

Solve for X:

$-22x+35-4x=31-8+10x$

Video Solution

Answer

$\frac{1}{3}$

Exercise #8

Solve for X:

$36x-52+8x=19x+54-31$

Video Solution

Answer

$3$

Exercise #9

Solve for X:

$-45+3x+99=5x+11x+2$

Video Solution

Answer

$4$

Exercise #10

Solve for X:

$54x-36x+34=39+5x-18$

Video Solution

Answer

$-1$

Question 1

Solve for X:

$\frac{3}{11}-\frac{8}{12}x+\frac{1}{3}x=\frac{1}{2}+\frac{2}{4}-\frac{22}{24}x$

Question 2

Solve for X:

$$ 0.3x-4.5+7.4x=3.8x-3.5+1.4 $$

Question 3

Solve for X:

$$ 7.21+11.5x-3.4x=8.11x-12.4+3.8 $$

Question 4

Solve for X:

$$ 7.23-14x+15.1x=3.1x-8.4 $$

Question 5

Solve for X:

$8.51x+\text{3}.4-6.14x=7.51+3.8x-6.1$

Exercise #11

Solve for X:

$\frac{3}{11}-\frac{8}{12}x+\frac{1}{3}x=\frac{1}{2}+\frac{2}{4}-\frac{22}{24}x$

Video Solution

Answer

$\frac{96}{77}$

Exercise #12

Solve for X:

$0.3x-4.5+7.4x=3.8x-3.5+1.4$

Video Solution

Answer

$0.61$

Exercise #13

Solve for X:

$7.21+11.5x-3.4x=8.11x-12.4+3.8$

Video Solution

Answer

$1581$

Exercise #14

Solve for X:

$7.23-14x+15.1x=3.1x-8.4$

Video Solution

Answer

$7.815$

Exercise #15

Solve for X:

$8.51x+\text{3}.4-6.14x=7.51+3.8x-6.1$

Video Solution

Answer

$1.39$

Question 1

Solve for X:

$\frac{100}{25}+\frac{144}{12}x-\frac{33}{11}=\frac{56}{8}x-\frac{35}{7}x+\frac{18}{2}$

Question 2

Solve for X:

$\frac{1}{7}-\frac{3}{5}x+\frac{1}{8}x=\frac{1}{9}+\frac{3}{9}-\frac{2}{10}x$

Question 3

Solve for X:

$\frac{1}{8}x-\frac{3}{4}+\frac{1}{9}=-\frac{2}{8}+\frac{3}{4}x-\frac{1}{2}x$

Question 4

Solve for X:

$\frac{36}{4}x+\frac{35}{7}-\frac{81}{9}x=\frac{16}{8}+\frac{45}{5}x-\frac{38}{19}$

Question 5

Solve for X:

$$ 8.15x-13.14+5=7.1-8.4x $$

Exercise #16

Solve for X:

$\frac{100}{25}+\frac{144}{12}x-\frac{33}{11}=\frac{56}{8}x-\frac{35}{7}x+\frac{18}{2}$

Video Solution

Answer

$\frac{4}{5}$

Exercise #17

Solve for X:

$\frac{1}{7}-\frac{3}{5}x+\frac{1}{8}x=\frac{1}{9}+\frac{3}{9}-\frac{2}{10}x$

Video Solution

Answer

$-\frac{760}{693}$

Exercise #18

Solve for X:

$\frac{1}{8}x-\frac{3}{4}+\frac{1}{9}=-\frac{2}{8}+\frac{3}{4}x-\frac{1}{2}x$

Video Solution

Answer

$-3\frac{1}{9}$

Exercise #19

Solve for X:

$\frac{36}{4}x+\frac{35}{7}-\frac{81}{9}x=\frac{16}{8}+\frac{45}{5}x-\frac{38}{19}$

Video Solution

Answer

$\frac{5}{9}$

Exercise #20

Solve for X:

$8.15x-13.14+5=7.1-8.4x$

Video Solution

Answer

$0.92$