Final answer:
The equation -2(5x+8)=14+6x can be solved by distributing, combining like terms, and isolating the variable x, resulting in x = -7.5.
Step-by-step explanation:
To solve the equation -2(5x+8)=14+6x, we need to apply the distributive property, combine like terms, and isolate the variable x. The steps are as follows:
Distribute the -2 across (5x + 8) to get -10x - 16.
Combine the -10x with the 6x on the other side of the equation to get -4x - 16 = 14.
Add 16 to both sides to isolate the -4x term, resulting in -4x = 30.
Finally, divide both sides by -4 to find the value of x, which gives us x = -7.5.
By carefully following the rules for operations with integers and the properties of equality, we can solve linear equations and find the value of the variable.