8 14 – 2(x + 8) = 5x – (3x – 34); Prove: r = -9 Statements
The Correct Answer and Explanation is:
Let’s solve the equation step-by-step:
Given:8⋅14−2(x+8)=5x−(3x−34)8 \cdot 14 – 2(x + 8) = 5x – (3x – 34)8⋅14−2(x+8)=5x−(3x−34)
Step 1: Simplify both sides.
First, simplify the left-hand side:8⋅14=1128 \cdot 14 = 1128⋅14=112−2(x+8)=−2x−16-2(x + 8) = -2x – 16−2(x+8)=−2x−16
So, the left side becomes:112−2x−16=5x−(3x−34)112 – 2x – 16 = 5x – (3x – 34)112−2x−16=5x−(3x−34)
Simplify further:96−2x=5x−(3x−34)96 – 2x = 5x – (3x – 34)96−2x=5x−(3x−34)
Now, simplify the right-hand side:5x−(3x−34)=5x−3x+34=2x+345x – (3x – 34) = 5x – 3x + 34 = 2x + 345x−(3x−34)=5x−3x+34=2x+34
Now the equation is:96−2x=2x+3496 – 2x = 2x + 3496−2x=2x+34
Step 2: Solve for xxx.
Move all terms involving xxx to one side, and constant terms to the other side.
First, add 2x2x2x to both sides:96=4x+3496 = 4x + 3496=4x+34
Now subtract 34 from both sides:62=4×62 = 4×62=4x
Finally, divide both sides by 4:x=624=15.5x = \frac{62}{4} = 15.5x=462=15.5
Conclusion:
The solution for xxx is 15.515.515.5, not r=−9r = -9r=−9. It seems there might be a typo or misunderstanding in the question. However, based on the algebraic steps, the correct value for xxx is 15.515.515.5.
