To solve the equation 10(-2x+1) = 19(x+1), follow these steps:
Step 1: Distribute
Multiply each term inside the parentheses by the number outside the parentheses. This gives us:
-20x + 10 = 19x + 19
Step 2: Combine like terms
Group all the x terms on one side and all the constant terms on the other side of the equation. Subtract 19x from both sides to get:
-20x - 19x + 10 = 19
Step 3: Combine like terms
Combine the x terms on the left side of the equation and the constant terms on the right side:
-39x + 10 = 19
Step 4: Subtract 10 from both sides
Subtract 10 from both sides of the equation to isolate the term with x:
-39x = 19 - 10
-39x = 9
Step 5: Divide by -39
Divide both sides of the equation by -39 to solve for x:
x = 9 / -39
Step 6: Simplify the fraction
Reduce the fraction 9 / -39 if possible:
x = -3 / 13
So the solution to the equation 10(-2x+1) = 19(x+1) is x = -3/13.
