Linear equation: -6w+16=2(-3w+8)?

-6w + 16 = 2 (-3w + 8)

-6w + 16 = -6w + 16

....... - 16............- 16

-6w = -6w

+6w...+6w

0=0

All real numbers work.

Reggie's Math Mini-Lessons--Distributive Property and Solving for x

PROBLEM / QUESTION:

How do I use the distributive property if its an equation with variables

REGGIE SAYS:

This explanation assumes you know the distributive property, so I will review it VERY briefly, then go on to the question listed.

Distributive Property Review

The distributive property can perhaps be best explained by an example:

3(4 + x) = 3 times 4 + 3 times x

So 3 * 4 + 3x = 12 + 3x.

We have distributed the three, or multiplied it by each of the terms in parentheses.

Using the Distributive Property when Solving an Equation:

When you have an equation, like the one below, where one or more terms looks like an expression you would simplify using the distributive property, and you are asked to solve for x, use the distributive property to simplify the terms, then solve like any other equation.

Guided example:

Solve for x.

3(x + 2) = 4x

1) Distribute the 3 to the x and the 2

3x + 3(2) = 6x

3x + 6 = 6x

2) Get your x terms on the same side then, if necessary, get non-variable terms on the same side so that you have variable terms on one side and non-variables on the other.

3x + 6 - 3x = 6x - 3x

3x - 3x reduces to zero

6 = 3x

3) If necessary, divide both sides by the coefficient of x (tha's the number that comes right before x).

6 / 3 = 3x / 3

3 = x

You try these (and no peeking at the answers below until you've done them):

1) 2(a + 7) = 14 - a

2) 6(m + 2) = 24

3) 3 (x + 1) = 2x

Answers/ solutions:

1) 2a + 14 = 14 - a

3a + 14 = 14

3a =0

a = 0

2) 6m + 12 = 24

6m = 12

m = 2

3) 3x + 3 = 2x

3x = 2x - 3

x = -3

OR

3x = 2x - 3

-x = 3

x = -3

Assignment:

--Do the problems you gave us.--

Hope this helps,

--Reggie

first make the parenthesis

-6w+16=2(-3w+8)

-6w+16=-6w+16 as you see you get the same equation

0=0 all real number works

Expand the terms on the right side of the equation

-6w + 16 = -6w + 16

Move the variable to one side of the equation, the constants to the other.

-6w + 6w = +16 - 16

w = 0

-6w + 16 = 2(-3w + 8)

Distribute

-6w + 16 = -6w + 16

Since these two sides are the same

Answer: All real numbers

Hope this helps you! Please email if you want further clarification.

-6w + 16 = -6w + 16

since both sides are equal, w can equal any value and the equation will be true

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