Solve the following equation for xx. Express your answer in the simplest form.
7, left bracket, minus, 7, x, minus, 1, right bracket, equals, minus, 5, left bracket, 5, x, minus, 8, right bracket
7(−7x−1)=
−5(5x−8)
Answer
Attempt 1 out of 2
The equation has
no solution
infinitely many solutions
one solution
.
one solution
The equation has
one solution
and it is x=
x = -1
7(−7x−1)= −5(5x−8)
-49 x - 7 = -25 x + 40
24 x = -47
x = -47/24
x = -47/24
To solve the equation, we need to simplify both sides separately and then equate them to each other. Let's start simplifying both sides of the equation:
On the left side:
7(-7x - 1) = -49x - 7
On the right side:
-5(5x - 8) = -25x + 40
Now, we set the two simplified sides equal to each other:
-49x - 7 = -25x + 40
Next, we want to isolate the x variable by moving all the terms containing x to one side of the equation:
-49x + 25x = 40 + 7
Simplifying further:
-24x = 47
Finally, we solve for x by dividing both sides of the equation by -24:
x = 47 / -24
This cannot be simplified any further, so the answer is x = -47/24.
So, the equation has one solution: x = -47/24.