Answer:
B. 5(x + 1) - 3x = 5 - 2(5 - x)
Step-by-step explanation:
A. x - 5(x - 4) = 2(2x + 7) + 6 Distribute -5 into parentheses
x - 5x + 20 = 2(2x +7) + 6 Distribute 2 into parentheses
x - 5x + 20 = 4x +14 + 6 Combine like terms (I underlined it to show)
-4x + 20 = 4x + 20
+4x +4x Do Inverse operations
20 = 8x + 20
-20 - 20 Do inverse operations
0 = 8x
[tex]\frac{0}{8}[/tex] = [tex]\frac{8x}{8}[/tex] Divide by 8 on both sides to isolate the variable.
0 = x
Solution is x = 0.
B. 5(x + 1) - 3x = 5 - 2(5 - x) Distribute 5 into parentheses
5x + 5 - 3x = 5 - 2(5 - x) Distribute -2 into parentheses
5x + 5 - 3x = 5 - 10 + 2x Combine Like terms (I underlined the like terms)
2x + 5 = -5 + 2x
+ 5 +5 Do inverse operations
2x + 10 = 2x
-2x -2x Do inverse operations
10 ≠ 0
No solution
C. 1 - 3(x+3) = 2(3x - 4) - 9x Distribute -3 into parentheses
1 - 3x - 9 = 2(3x - 4) - 9x Distribute 2 into parentheses
1 - 3x - 9 = 6x - 8 - 9x Combine Like terms (I underlined the like terms)
- 8 - 3x = -3x - 8
+ 3x +3x Do inverse operations
- 8 = - 8
Solution = All real numbers
D. 3(x - 4) + x = 4(3 - x) Distribute 3 into parentheses
3x - 12 + x = 4(3 - x) Distribute 4 into parentheses
3x - 12 + x = 12 - 4x Combine Like terms (I underlined the like terms)
4x - 12 = 12 - 4x
+4x + 4x Do inverse operations
8x - 12 = 12
+ 12 +12 Do inverse operations
8x = 24
[tex]\frac{8x}{8}[/tex] = [tex]\frac{24}{8}[/tex] Divide by 8 on both sides to isolate the variable
x = 3
Solution is x = 3 .
So the only equation that has no solution is B. 5(x + 1) - 3x = 5 - 2(5 - x).
