Question

question
solve the following equation for x. express your answer in the simplest form.
-3(-7x - 7) = -35x - 35
answer attempt 1 out of 2
the equation has
o solution
infinitely many solutions
one solution
submit answer

Explanation:

Step1: Expand the left side

First, we expand \(-3(-7x - 7)\) using the distributive property \(a(b + c)=ab+ac\). Here, \(a = - 3\), \(b=-7x\) and \(c = - 7\). So we have \(-3\times(-7x)+(-3)\times(-7)=21x + 21\). The equation becomes \(21x+21=-35x - 35\).

Step2: Move all x terms to one side

Add \(35x\) to both sides of the equation: \(21x+35x + 21=-35x+35x - 35\). This simplifies to \(56x+21=-35\).

Step3: Move constant terms to the other side

Subtract 21 from both sides: \(56x+21 - 21=-35 - 21\). So \(56x=-56\).

Step4: Solve for x

Divide both sides by 56: \(x=\frac{-56}{56}=- 1\). Since we can find a unique value for \(x\), the equation has one solution.

Answer:

one solution