Let's solve the equations step by step:
1) 3x + 8(x - 1) = 47
First, distribute the 8:
3x + 8x - 8 = 47
Combine like terms:
11x - 8 = 47
Now, isolate the variable by adding 8 to both sides:
11x = 55
Finally, divide both sides by 11 to solve for x:
x = 5
Therefore, the solution to the first equation is x = 5.
2) 1/2(x + 2) = 5(x + 2)
First, distribute the 5 on the right side:
1/2(x + 2) = 5x + 10
Now, distribute the 1/2 on the left side:
1/2 * x + 1/2 * 2 = 5x + 10
Simplifying the equation:
1/2x + 1 = 5x + 10
Subtract 1/2x from both sides:
1 = 9.5x + 10
Subtract 10 from both sides:
-9 = 9.5x
Finally, divide both sides by 9.5 to solve for x:
x = -9/9.5 ≈ -0.947
Therefore, the solution to the second equation is x ≈ -0.947.
If you have any further questions, feel free to ask!