Problem 102
Question
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{3 x+1}{3}=x+1$$
Step-by-Step Solution
Verified Answer
The original statement \(\frac{3 x+1}{3}=x+1\) is False. The correct version of the statement is \(\frac{3 x+1}{3}=x+1/3\).
1Step 1: Analyze Equation
The given equation is \(\frac{3 x+1}{3}=x+1\). In order to determine the validity of this statement, try simplifying the left hand side of the equation to match the right hand side.
2Step 2: Simplify and Compare
Start by distributing 1/3 in the numerator of the left-hand side, which results in \(x+1/3\). Now, this is obviously not equivalent to \(x+1\) on the right hand side. Therefore, the original statement is false.
3Step 3: Correction
To correct the statement, we can equate the left hand side of the equation with its directly simplified form on the right hand side. So, the correct statement would be \(\frac{3 x+1}{3}=x+1/3\).
Other exercises in this chapter
Problem 100
Will help you prepare for the materia$l covered in the next section. Simplify: $$\frac{x^{2}-6 x+9}{x^{2}-9}$$
View solution Problem 102
perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{1}{2}+\frac{2}{3}$$
View solution Problem 103
perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{1}{8}-\frac{5}{6}$$
View solution Problem 103
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{x^{2}+3}{3}=x^{2
View solution