Question

solve each of these equations. explain or show your reasoning in the spa
a. \\(2b + 8 - 5b + 3 = -13 + 8b - 5\\)

Explanation:

Step1: Combine like terms on both sides

Left side: \(2b - 5b + 8 + 3 = -3b + 11\)
Right side: \(-13 - 5 + 8b = 8b - 18\)
So the equation becomes \(-3b + 11 = 8b - 18\)

Step2: Move all b terms to one side and constants to the other

Add \(3b\) to both sides: \(-3b + 3b + 11 = 8b + 3b - 18\)
Which simplifies to \(11 = 11b - 18\)
Then add 18 to both sides: \(11 + 18 = 11b - 18 + 18\)
So \(29 = 11b\)

Step3: Solve for b

Divide both sides by 11: \(b = \frac{29}{11}\)

Answer:

\(b = \frac{29}{11}\)