how do you solve 2 – 2n = 3n + 17
The correct answer and explanation is:
Let’s solve the equation step-by-step:
Equation:
2−2n=3n+172 – 2n = 3n + 17
Step 1: Get all terms with nn on one side
We want to gather all terms involving nn on one side and constants on the other.
Add 2n2n to both sides to move −2n-2n to the right: 2=3n+17+2n2 = 3n + 17 + 2n
Simplify the right side: 2=5n+172 = 5n + 17
Step 2: Isolate the term with nn
Subtract 17 from both sides: 2−17=5n+17−172 – 17 = 5n + 17 – 17 −15=5n-15 = 5n
Step 3: Solve for nn
Divide both sides by 5: −155=n\frac{-15}{5} = n n=−3n = -3
Final Answer:
n=−3\boxed{n = -3}
Explanation (300 words):
This is a linear equation in one variable, nn. The goal is to isolate nn on one side of the equation so we can find its value.
The original equation is 2−2n=3n+172 – 2n = 3n + 17. Here, 22 and 1717 are constants, while −2n-2n and 3n3n are terms with nn.
First, we want to collect all nn terms on one side to simplify the equation. Adding 2n2n to both sides eliminates the −2n-2n from the left, combining like terms on the right: 2=3n+17+2n2 = 3n + 17 + 2n
Simplifying the right side gives: 2=5n+172 = 5n + 17
Next, we move the constant term 1717 to the left side by subtracting 17 from both sides, isolating the term with nn: 2−17=5n2 – 17 = 5n −15=5n-15 = 5n
Finally, to solve for nn, divide both sides by the coefficient of nn, which is 5: n=−155=−3n = \frac{-15}{5} = -3
The solution means that when n=−3n = -3, both sides of the original equation are equal.
You can verify this by substituting n=−3n = -3 back into the original equation:
Left side: 2−2(−3)=2+6=82 – 2(-3) = 2 + 6 = 8
Right side: 3(−3)+17=−9+17=83(-3) + 17 = -9 + 17 = 8
Since both sides equal 8, n=−3n = -3 is the correct solution.