Question

7(r-2) - 9(r-1) = 3(5-r) + r- 8)

a) No solution
b) All real numbers
c) 0
d) -5

Answer 1

The question involves solving a linear equation for the variable 'r'. This includes expanding, combining like terms, and solving for 'r' using basic algebraic principles.

Step-by-step explanation:

The question provided is a linear equation where you are asked to solve for 'r'. To find the value of 'r', we need to expand the brackets, combine like terms, and solve for 'r'. We do so by applying the distributive property and collecting like terms.

Let's go through this step by step:

1. Expand both sides of the equation by distributing the numbers outside the brackets.
2. Combine all the 'r' terms on one side and the constant terms on the other side.
3. Simplify by adding or subtracting terms as necessary.
4. Divide by the coefficient of 'r' if it is not equal to 1, to solve for 'r'.

Once we've done this for the provided equation, we'll find the value for 'r' that satisfies the equation or determine if there is no solution, or if all real numbers are a solution.