Examples with solutions for Solving Equations Using All Methods: One sided equations

Exercise #1

Solve for X:

2+x5=43 2 + x - 5 = 4 - 3

Step-by-Step Solution

To solve2+x5=43 2 + x - 5 = 4 - 3 , we first simplify both sides:

Left side:
25+x=3+x 2 - 5 + x = -3 + x

Right side:
43=1 4 - 3 = 1

Now the equation is 3+x=1 -3 + x = 1 .

Add 3 to both sides:
x=1+3 x = 1 + 3

So,x=4 x = 4 .

Answer

4

Exercise #2

Solve for X:

3x=106 3 - x = 10 - 6

Step-by-Step Solution

First, simplify the right side of the equation:
106=4 10 - 6 = 4
Hence, the equation becomes 3x=4 3 - x = 4 .
Subtract 3 from both sides to isolate x x :
3x3=43 3 - x - 3 = 4 - 3
This simplifies to:
x=1 -x=1
Divide by -1 to solve forx x :
x=1 x=-1
Therefore, the solution is x=1 x = 1 .

Answer

-1

Exercise #3

Solve for X:

3+x+1=62 3 + x + 1 = 6 - 2

Step-by-Step Solution

To solve 3+x+1=62 3 + x + 1 = 6 - 2 , we first simplify both sides:

Left side:
3+1+x=4+x 3 + 1 + x = 4 + x

Right side:
62=4 6 - 2 = 4

Now the equation is 4+x=4 4 + x = 4 .

Subtract 4 from both sides:
x=44 x = 4 - 4

So, x=0 x = 0 .

Answer

0

Exercise #4

Solve for X:

3+x2=73 3 + x - 2 = 7 - 3

Step-by-Step Solution

First, simplify both sides of the equation:

Left side: 3+x2=1+x 3 + x - 2 = 1 + x

Right side: 73=4 7 - 3 = 4

So the equation becomes:

1+x=4 1 + x = 4

Next, isolate x x by subtracting 1 from both sides:

1+x1=41 1 + x - 1 = 4 - 1

This simplifies to:

x=3 x = 3

Answer

3

Exercise #5

Solve for X:

5x=124 5 - x = 12 - 4

Step-by-Step Solution

First, simplify the right side of the equation:
124=8 12 - 4 = 8
Hence, the equation becomes 5x=8 5 - x = 8 .
Subtract 5 from both sides to isolate x x :
5x5=85 5 - x - 5 = 8 - 5
This simplifies to:
x=3 -x=3
Divide by -1 to solve for x x :
x=3 x=-3
Therefore, the solution is x=3 x=-3 .

Answer

-3

Exercise #6

Solve for X:

5+x3=2+1 5 + x - 3 = 2 + 1

Step-by-Step Solution

To solve 5+x3=2+1 5 + x - 3 = 2 + 1 , we first simplify both sides:

Left side:
53+x=2+x 5 - 3 + x = 2 + x

Right side:
2+1=3 2 + 1 = 3

Now the equation is 2+x=3 2 + x = 3 .

Subtract 2 from both sides:
x=32 x = 3 - 2

So, x=1 x = 1 .

Answer

1

Exercise #7

Solve for X:

6x=102 6 - x = 10 - 2

Step-by-Step Solution

To solve the equation 6x=102 6 - x = 10 - 2 , follow these steps:

  1. First, simplify both sides of the equation:

  2. On the right side, calculate 102=8 10 - 2 = 8 .

  3. The equation simplifies to 6x=8 6 - x = 8 .

  4. To isolate x, subtract 6 from both sides:

  5. 6x6=86 6 - x - 6 = 8 - 6

  6. This simplifies to x=2 -x = 2 .

  7. Multiply both sides by -1 to solve for x:

  8. x=2×1=2 x = -2 \times -1 = 2 .

  9. Since the problem requires only manipulation by transferring terms, the initial approach to the equation setup should lead to x = 4 as the solution before re-evaluation.

Therefore, the correct solution to the equation is x=2 x=2 .

Answer

2

Exercise #8

Solve for X:

7x=155 7 - x = 15 - 5

Step-by-Step Solution

First, simplify the right side of the equation:
155=10 15 - 5 = 10
Hence, the equation becomes 7x=10 7 - x = 10 .
Subtract 7 from both sides to isolate x x :
7x7=107 7 - x - 7 = 10 - 7
This simplifies to:
x=3 -x=3
Divide by -1 to solve forx x :
x=3 x=-3
Therefore, the solution is x=3 x=-3 .

Answer

-3

Exercise #9

Solve for X:

8x=113 8 - x = 11 - 3

Step-by-Step Solution

First, simplify the right side of the equation:
113=8 11 - 3 = 8
Hence, the equation becomes 8x=8 8 - x = 8 .
Subtract 8 from both sides to isolate x x :
8x8=88 8 - x - 8 = 8 - 8
This simplifies to:
x=0 -x=0
Divide by -1 to solve for x x :
x=0 x = 0
Therefore, the solution is x=0 x = 0 .

Answer

0

Exercise #10

Solve for X:

9x=167 9 - x = 16 - 7

Step-by-Step Solution

First, simplify the right side of the equation:
167=9 16 - 7 = 9
Hence, the equation becomes 9x=9 9 - x = 9 .
Since both sides are equal, x x must be 0 0 .
Therefore, the solution is x=0 x = 0 .

Answer

0

Exercise #11

Solve for X:

x3+5=82 x - 3 + 5 = 8 - 2

Step-by-Step Solution

First, simplify both sides of the equation:

Left side: x3+5=x+2 x - 3 + 5 = x + 2

Right side: 82=6 8 - 2 = 6

Now the equation is: x+2=6 x + 2 = 6

Subtract 2 from both sides to isolate x x :

x+22=62 x + 2 - 2 = 6 - 2

Simplifying gives:

x=4 x = 4

Answer

4

Exercise #12

Solve for X:

x+42=6+1 x + 4 - 2 = 6 + 1

Step-by-Step Solution

First, simplify both sides of the equation:

Left side: x+42=x+2 x + 4 - 2 = x + 2

Right side: 6+1=7 6 + 1 = 7

Now the equation is: x+2=7 x + 2 = 7

Subtract 2 from both sides to isolatex x :

x+22=72 x + 2 - 2 = 7 - 2

Simplifying gives:

x=5 x = 5

Answer

5

Exercise #13

Solve for X:

5x+10=3x+18 5x + 10 = 3x + 18

Step-by-Step Solution

To solve the equation 5x+10=3x+18 5x + 10 = 3x + 18 , follow these steps:

1. Subtract 3x 3x from both sides to get:

5x3x+10=18 5x - 3x + 10 = 18

2. Simplify the equation:

2x+10=18 2x + 10 = 18

3. Subtract 10 10 from both sides:

2x=8 2x = 8

4. Divide both sides by 2 2 :

x=4 x = 4

Answer

4

Exercise #14

Solve for X:

7x3=4x+9 7x - 3 = 4x + 9

Step-by-Step Solution

To solve the equation 7x3=4x+9 7x - 3 = 4x + 9 , follow these steps:

1. Subtract 4x 4x from both sides to get:

7x4x3=9 7x - 4x - 3 = 9

2. Simplify the equation:

3x3=9 3x - 3 = 9

3. Add 3 3 to both sides:

3x=12 3x = 12

4. Divide both sides by 3 3 :

x=4 x=4

Answer

4

Exercise #15

Find the value of the parameter X

8x=5 -8-x=5

Video Solution

Answer

13 -13

Exercise #16

Find the value of the parameter X:

x+5=8 x+5=8

Video Solution

Answer

3

Exercise #17

Solve for X:

3+x=4 3+x=4

Video Solution

Answer

1

Exercise #18

Solve for X:

3x+7=5 3-x+7=5

Video Solution

Answer

5

Exercise #19

Solve for X:

5+x=3 -5+x=-3

Video Solution

Answer

2 2

Exercise #20

Solve for X:

5x=4 5-x=4

Video Solution

Answer

1