Question

`\mathrm{6(2x-4)=10(x+2)}`

Answer 1

x = 22

Explanation:

Solve for x:

6 (2 x - 4) = 10 (x + 2)

Expand out terms of the left hand side:

(12 x - 24) = 10 (x + 2)

Expand out terms of the right hand side:

12 x - 24 = (10 x + 20)

Subtract 10 x from both sides:

(12 x - 10 x) - 24 = (10 x - 10 x) + 20

12 x - 10 x = 2 x:

2 x - 24 = (10 x - 10 x) + 20

10 x - 10 x = 0:

2 x - 24 = 20

Add 24 to both sides:

2 x + (24 - 24) = 24 + 20

24 - 24 = 0:

2 x = 20 + 24

20 + 24 = 44:

2 x = 44

Divide both sides of 2 x = 44 by 2:

(2 x)/2 = 44/2

2/2 = 1:

x = 44/2

The gcd of 44 and 2 is 2, so 44/2 = (2×22)/(2×1) = 2/2×22 = 22:

Answer: x = 22

Answer 2

22

Explanation:

To solve for x in the equation 6(2x - 4) = 10(x + 2), we can start by distributing the 6 and 10 on the left and right side of the equation respectively:

12x - 24 = 10x + 20

Next, we can combine like terms by adding x to both sides and subtracting 24 from both sides:

12x - 24 + 24 = 10x + 20 + 24

12x = 10x + 44

subtracting both side by 10x

12x-10x=10x-10x+44

2x=44

x=44/2

x=22