#### Question

1. Solve for x: 3x ? 5 = 2x + 6

1

?1

11

?11

2. Solve for x: ?2(x + 3) = ?4(x ? 6)

?5

15

?15

30

3. Solve for x: 3(x + 1) = ?2(x ? 1) ? 4

1

?1

?5

?25

4. Solve for x: ?3(x + 3) = ?3(x + 1) ? 5

6

?6

All real numbers

No solution

5. Create your own two-step equation with NO SOLUTION as the solution. Show the steps to solving the equation and explain in words why your work proves that there are NO SOLUTIONS.

1. 3x ? 5 = 2x + 6

Subtract both sides by 2x:

3x - 2x - 5 = 6

x - 5 = 6

x - 5 + 5 = 6 + 5

x = 11

2. ?2(x + 3) = ?4(x ? 6)

Distribute -2 into x + 3 and -4 into x - 6:

-2x - 6 = -4x + 24

-2x + 4x - 6 = -4x + 4x + 24

2x - 6 = 24

2x - 6 + 6 = 24 + 6

2x = 30

Divide both sides by 2:

2x/2 = 30/2

x = 15

3. 3(x + 1) = ?2(x ? 1) ? 4

Distribute 3 into x + 1 and -2 into x - 1:

3x + 3 = -2x + 2 - 4

Combine like terms:

3x + 3 = -2x - 2

3x + 2x + 3 = -2x + 2x - 2

5x + 3 = -2

Subtract both sides by 3:

5x - 3 + 3 = -2 - 3

5x = -5

Divide both sides by 5:

5x/5 = -5/5

x = -1

4. -3(x + 3) = -3(x + 1) - 5

Note that this problem is similar to the third!

-3x - 9 = -3x - 3 - 5

-3x - 9 = -3x - 8

No solution since you have same 3x's but different constant. Hence, there is no solution for this problem.

5. 3x + 4 = 3x - 2

Same as problem #4. If you rearrange the terms, then you get:

0x = 6

x = 6/0

x = undefined

I hope this helps!

#1