Question

5x+x=6; 7x+x+3=19; 8=3x-x; 3x-6x=x; 3-x=1+x;5x-8=3x-8; 5x-2 1/4=1/2; 2x-3/5=3/4x-1/2

Answer 1

1. 6x=6
x=6:6
x=1
2. 8x=19-3
8x=16
x=16:8
x=2
3. 8=2x
x=8:2
x=4
4. 3x-6x=x
-3x-x=0
-4x=0
x=0
5. 3-1=2x
2x=2
x=2:2
x=1
6. 5x-3x=-8+8
2x=0
x=0
7. 5x=1/2+2 1/4 
5x=2,75
x=2,75:5
x=0,55
8.  2x+3/4x=-1/2+3/5
2,75x=0.1
x=0,1:2,75
x=2/55

Answer 2

To solve each of these equations, we'll go through them one by one and apply the necessary steps to isolate the variable.

Equation 1: 5x + x = 6

Combining like terms on the left side gives us: 6x = 6

To isolate x, we divide both sides of the equation by 6: (6x)/6 = 6/6 x = 1

So the solution to the equation 5x + x = 6 is x = 1.

Equation 2: 7x + x + 3 = 19

Combining like terms on the left side gives us: 8x + 3 = 19

To isolate x, we subtract 3 from both sides of the equation: 8x + 3 - 3 = 19 - 3 8x = 16

Next, we divide both sides of the equation by 8: (8x)/8 = 16/8 x = 2

So the solution to the equation 7x + x + 3 = 19 is x = 2.

Equation 3: 8 = 3x - x

Combining like terms on the right side gives us: 8 = 2x

To isolate x, we divide both sides of the equation by 2: (8)/2 = 2x/2 4 = x

So the solution to the equation 8 = 3x - x is x = 4.

Equation 4: 3x - 6x = x

Combining like terms on the left side gives us: -3x = x

To isolate x, we add 3x to both sides of the equation: -3x + 3x = x + 3x 0 = 4x

Since any number multiplied by zero is zero, the equation -3x = x has no solution.

Equation 5: 3 - x = 1 + x

To isolate x, we need to get rid of the x term on the right side of the equation.

First, let's get rid of the x term on the left side by adding x to both sides: 3 - x + x = 1 + x + x 3 = 1 + 2x

Next, let's get rid of the constant term on the right side by subtracting 1 from both sides: 3 - 1 = 1 + 2x - 1 2 = 2x

To isolate x, we divide both sides of the equation by 2: (2)/2 = (2x)/2 1 = x

So the solution to the equation 3 - x = 1 + x is x = 1.

Equation 6: 5x - 8 = 3x - 8

To isolate x, we need to get rid of the constant term on both sides of the equation.

Subtracting 3x from both sides gives us: 5x - 3x - 8 = 3x - 3x - 8 2x - 8 = 0

Next, let's get rid of the constant term on the left side by adding 8 to both sides: 2x - 8 + 8 = 0 + 8 2x = 8

To isolate x, we divide both sides of the equation by 2: (2x)/2 = 8/2 x = 4

So the solution to the equation 5x - 8 = 3x - 8 is x = 4.

Equation 7: 5x - 2 + 1/4 = 1/2

To isolate x, we need to get rid of the constant terms on both sides of the equation.

First, let's simplify the equation by adding the fractions together: 5x - 2 + 1/4 = 1/2 5x - 2 + 1/4 = 2/4

Next, let's find a common denominator for the fractions on the left side, which is 4: 5x - 2 + (1/4)*4 = (2/4)*4 5x - 2 + 1 = 2

Simplifying further: 5x - 1 = 2

To isolate x, we add 1 to both sides of the equation: 5x - 1 + 1 = 2 + 1 5x = 3

Finally, we divide both sides of the equation by 5 to solve for x: (5x)/5 = 3/5 x = 3/5

So the solution to the equation 5x - 2 + 1/4 = 1/2 is x = 3/5.

Equation 8: 2x - 3/5 = 3/4x - 1/2

To isolate x, we need to get rid of the variable terms on both sides of the equation.

First, let's simplify the equation by finding a common denominator for the fractions: 2x - 3/5 = (3/4)x - 1/2 2x - 3/5 = (15/20)x - 10/20

Next, let's combine the variable terms on the right side: 2x - 3/5 = (15/20)x - 10/20 2x - (15/20)x = -10/20 + 3/5

Simplifying further: (40/20)x - (15/20)x = -10/20 + 6/20 (25/20)x = -4/20

To isolate x, we multiply both sides of the equation by the reciprocal of (25/20), which is (20/25) or (4/5): ((25/20)x) * (20/25) = (-4/20) * (20/25) x = -4/25

So the solution to the equation 2x - 3/5 = 3/4x - 1/2 is x = -4/25.

I hope this helps! Let me know if you have any further questions.