Solution sets of given equations?

Question

(x - 3) - 2(x + 6) = -5

1. {-10}

2. {-4}

3. {8}

14 + 8m = 14 - 3m - 5m

1. Ø

2. {0}

3. {all reals}

Answer 1

2. {-4}

1. Ø

Answer 2

Answer for the first question is....

1. {-10}

And for the second question is...

1. Ø

Explanations~

Question #1

(x-3)-2(x+6)           = -5   First, simply the equation.

The roughly simplified equation would be;

x-3-2x-12 = -5 because when u simplify the part -2(x+6), there's a negative sign in front of the 2 so the answer has to be negative even though there's a positive sign inside the brackets.

x-3-2x-12  = -5    Then simplify the equation THOROUGHLY.

-x-15         = -5    Get variables on one side and numbers on the other.

-x-15+15  = -5+15 Wateva u do to one side, u have to do it to the other as well.

-x  = 10 But since the x has a negative sign in front, 10 is not the final answer so multiply both sides by a negative sign.

-x * (-) = 10 * (-)

x  = -10 would be the final answer for Question #1.

Question #2

14 + 8m = 14 - 3m - 5m  First simplify the equation.

14 + 8m = 14 - 8m

As u can see above, there're equal amount of variables and numbers with exactly the same amount. If u see an equation like that, it CANNOT be solved. If u don't believe me, try asking ur parents or ur teacher. ^-^

Answer 3

Ans:

Q1: 2.{-4}

Q2: 3.{all reals}

Solution

Simplify the equations to get

in q1:

x-2x = -5 +6+3

=> -x = 4

=> x=-4

in q2:

14-14 = 8m - 8m

=> 0 = 0m

This is true for all m, i.e. all real values of m so the answer is 3. {all reals}