Questions: Solve this equation and enter your answer in the box. Make sure your answer is fully reduced. If the answer turns out to be a false equation or identity, click on the appropriate button. [ (x+10)/2=7(x-1) ]

Solve this equation and enter your answer in the box. Make sure your answer is fully reduced. If the answer turns out to be a false equation or identity, click on the appropriate button.
[
(x+10)/2=7(x-1)
]

Transcript text: Solve this equation and enter your answer in the box. Make sure your answer is fully reduced. If the answer turns out to be a false equation or identity, click on the appropriate button. \[ \frac{x+10}{2}=7(x-1) \]

Solution

Solution Steps

To solve the equation \(\frac{x+10}{2}=7(x-1)\), we need to first eliminate the fraction by multiplying both sides by 2. Then, we expand and simplify the equation to isolate \(x\). Finally, we solve for \(x\) and check if the solution is valid or if the equation is an identity or a false equation.

Step 1: Eliminate the Fraction

Starting with the equation

\[ \frac{x+10}{2} = 7(x-1), \]

we multiply both sides by 2 to eliminate the fraction:

\[ x + 10 = 14(x - 1). \]

Step 2: Expand and Simplify

Next, we expand the right side of the equation:

\[ x + 10 = 14x - 14. \]

Now, we rearrange the equation to isolate \(x\):

\[ 10 + 14 = 14x - x, \]

which simplifies to

\[ 24 = 13x. \]