Question

Algebra2 help please!?

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.

Answers

1. 3x ? 5 = 2x + 6

Subtract both sides by 2x:

3x - 2x - 5 = 6

x - 5 = 6

Add both sides by 5:

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

Add both sides by 4x:

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

2x - 6 = 24

Add both sides by 6:

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

Add both sides by 2x:

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