Solve for r.
18r-10r-20r+2r+9r=18
The correct answer and explanation is:
The given equation is: 18r−10r−20r+2r+9r=1818r – 10r – 20r + 2r + 9r = 18
Step 1: Combine like terms on the left-hand side.
Group all the terms with rr: (18r−10r−20r+2r+9r)(18r – 10r – 20r + 2r + 9r)
Now, perform the addition/subtraction for the coefficients of rr: 18r−10r=8r18r – 10r = 8r 8r−20r=−12r8r – 20r = -12r −12r+2r=−10r-12r + 2r = -10r −10r+9r=−r-10r + 9r = -r
So, the equation simplifies to: −r=18-r = 18
Step 2: Solve for rr.
Now, to isolate rr, multiply both sides of the equation by -1: r=−18r = -18
Conclusion:
The value of rr is −18-18.
Explanation:
In this problem, we used basic algebraic principles to combine like terms and simplify the equation. Combining terms means adding or subtracting the coefficients of similar variables (in this case, all the terms contain the variable rr). Once we simplified the left-hand side of the equation to −r-r, we isolated rr by multiplying both sides of the equation by −1-1, giving us the final solution r=−18r = -18. This approach can be applied to any similar equation involving variables.