Final answer:
The solution for the given equations 5(x-3) = 2x + 6 is x=7.
Step-by-step explanation:
To solve the equation 5(x-3) = 2x + 6, follow these steps:
Distribute the 5 into the parentheses: 5 * x - 5 * 3 = 2x + 6
Which simplifies to 5x - 15 = 2x + 6
Eliminate terms wherever possible to simplify the algebra.
Subtract 2x from both sides: 5x - 2x - 15 = 6
Which simplifies to 3x - 15 = 6
Add 15 to both sides to isolate the term with the variable:
3x - 15 + 15 = 6 + 15
Which simplifies to 3x = 21
Divide both sides by 3 to solve for x:
3x/3 = 21/3
Which gives us x = 7
Check the answer to see if it is reasonable by substituting back into the original equation: 5(7-3) = 2*7 + 6, which indeed simplifies to 5*4 = 14 + 6, and further to 20 = 20, confirming our solution is correct.
Therefore, the solution for the given equations is x=7.