Question

1. Select all the equations that have no solution.

a. +6=5+
b. -2(−3)=-2+6
c. 4−4=3+2
d. 4(+1)=3(+2)
e. 5−3=-3+4

Answer 1

a, and e.

Explanation:

x+6=5+x has no solution. When you subtract 6 from both sides, you get x=-1+x. We know that x doesn't equal -1+x, so this equation has no solution.

-2(x-3)=-2x+6 has a solution. When you distribute, you get -2x+6=-2x+6.

4-4x=3x+2 has a solution. Subtract 4 from both sides to get -4x=3x-2. Subtract 3x from both sides to get -7x=-2, then divide -2 by -7 to get x=0.285714285714. This equation has a solution.

4(x+1)=3(x+2) has a solution. Distribute to get 4x+4=3x+6. Subtract 4 from both sides to get 4x=3x+2. Subtract 3x from both sides to get x=2. This equation has a solution.

5-3x=-3x+4 has no solution. Subtract 5 from both sides to get -3x=-3x-1. We know that -3x does not equal -3x-1, so we can determine that this equation has no solution.

Answer 2

a and e has no solution

Explanation:

A) x + 6 = x +5

Subtract x from both sides

x + 6 - x = x + 5 - x

6 = 5 which is not true.

So, this equation has no solution

d) 5 - 3x = -3x + 4

Add 3x to both sides

5- 3x + 3x = -3x + 4 + 3x

5 = 4 which is not true.

So, no solution