Question

How many solutions exist for the given equation? StartFraction one-half left-parenthesis x plus 12 right-parenthesis equals 4 x minus 1.(x + 12) = 4x – 1 zero one two infinitely many

Answer 1

One solution x = 2

Explanation:

Given the equation:

`(1)/(2)(x+12)=4x-1`

Multiply this equation by 2:

`2\cdot (1)/(2)(x+12)=2\cdot (4x-1)\\ \\x+12=2(4x-1)`

Use distributive property:

`x+12=8x-2`

Combine the like terms:

`x+12=8x-2\\ \\x+12-12=8x-2-12\\ \\x=8x-14\\ \\x-8x=8x-14-8x\\ \\-7x=-14\\ \\7x=14\\ \\x=2`

Thus, this equation has one solution x = 2