solve the equation and check
-(9x-4)-(2x-6)+7=-8(x-9)-(6x+2)+4
What don't you understand about this problem?
How far have you gotten with solving it?
I'll be glad to help you if I know more about your thinking on it.
i keep coming up with the solution is equal to all real numbers
Please post your work. I'll try to critique it.
To solve the equation, let's simplify each side step by step.
Starting with the left side of the equation:
-(9x-4) -(2x-6) + 7 = -8(x-9) -(6x+2) + 4
When simplifying expressions within parentheses, you can distribute the negative sign (-) to each term within the parentheses.
-(9x-4) becomes -9x + 4
-(2x-6) becomes -2x + 6
Now the equation looks like:
-9x + 4 + (-2x + 6) + 7 = -8(x-9) -(6x+2) + 4
Next, combine like terms on the left side of the equation:
-9x + 4 - 2x + 6 + 7 = -8(x-9) -(6x+2) + 4
-11x + 17 = -8(x-9) - (6x+2) + 4
Now let's simplify the right side of the equation:
To distribute -8 to (x-9), we will multiply -8 by each term within the parentheses:
-8(x-9) becomes -8x + 72
To distribute -1 to (6x+2), we will multiply -1 by each term within the parentheses:
-(6x+2) becomes -6x - 2
Now the equation becomes:
-11x + 17 = -8x + 72 - 6x - 2 + 4
Combine like terms on the right side of the equation:
-11x + 17 = -8x - 6x + 72 - 2 + 4
-11x + 17 = -14x + 74
To isolate x, we want all terms containing x to be on one side of the equation and constants on the other side.
Let's move all terms containing x to the left side by adding 14x to both sides:
-11x + 14x + 17 = -14x + 14x + 74
Combine like terms:
3x + 17 = 74
Next, subtract 17 from both sides of the equation:
3x + 17 - 17 = 74 - 17
3x = 57
Finally, divide both sides of the equation by 3 to solve for x:
3x/3 = 57/3
x = 19
Now that we have found the solution x = 19, we can check our answer by substituting it back into the original equation and verifying that both sides match:
-(9x-4) -(2x-6) + 7 = -8(x-9) -(6x+2) + 4
Substituting x = 19:
-(9(19)-4) -(2(19)-6) + 7 = -8(19-9) -(6(19)+2) + 4
Simplifying both sides:
-171 + 4 - 38 + 6 + 7 = -8*10 - 114 + 4
-125 = -80 - 110
-125 = -190
The equation is not true when x = 19, which means that our initial solution is incorrect.
Therefore, there is no solution to the equation.