Question

svlc algebra 1a - standard (15260) solving linear equations: distributive property how many solutions exist for the given equation? 3(x - 2) = 22 - x infinitely many two zero one

Explanation:

Step1: Apply distributive property

First, we apply the distributive property to the left side of the equation \(3(x - 2)\). The distributive property states that \(a(b - c)=ab - ac\), so for \(a = 3\), \(b=x\), and \(c = 2\), we get:
\(3(x - 2)=3x-3\times2 = 3x - 6\)
So the equation becomes \(3x - 6=22 - x\).

Step2: Add \(x\) to both sides

To get all the \(x\) terms on one side, we add \(x\) to both sides of the equation. Adding \(x\) to the left side: \(3x+x-6 = 4x - 6\). Adding \(x\) to the right side: \(22 - x+x=22\). So now the equation is \(4x - 6 = 22\).

Step3: Add 6 to both sides

Next, we add 6 to both sides to isolate the term with \(x\). Adding 6 to the left side: \(4x-6 + 6=4x\). Adding 6 to the right side: \(22+6 = 28\). So the equation becomes \(4x=28\).

Step4: Solve for \(x\)

To solve for \(x\), we divide both sides by 4. \(\frac{4x}{4}=\frac{28}{4}\), which simplifies to \(x = 7\). Since we found a unique value for \(x\) that satisfies the equation, there is one solution.

Answer:

one