x+6=3(5-x)

Question

slove please

 

Answer 1

X+6=3(5-x) distributive property

X+6=15-3x add 3x and subtract 6 from either side

4x=9 divide by 4 to get 1x

X=(9/4) or 2.25

Answer 2

There are several acceptable ways to solve this problem, though Raymond Y's is probably the most common (note-if you are expected to show your work and do one step at a time, as most teachers want, then seperate the +3x and -6 into 2 seperate steps).

Here are 4 ways I would accept from my students, as a teacher:

Ways #1 & 2

(with the Distributive Property)

x+6 = 3(5-x)  Distribute the 3

x+6 = 15-3x

Using 2 seperate steps, and in either order, pick whether to +3x & -6 to each side (way 1) OR -x & -15 from each side (way 2).  The variables and constants end up on opposite sides with the 2 ways, but both are ok.

Way 1                                     Way 2

x+6 = 15-3x   (+3x & -6)        x+6 = 15-3x    (-x & -15)

4x = 9                                      -9 = -4x 

Divide each side by 4.            Divide each side by -4.  

1x = 9/4  OR  x = 9/4              -9/-4 = -4x/-4  simplifies to 9/4 = 1x  OR  9/4 = x

(or 2.25 if you divide it to a decimal)

Ways #3 & 4

(without the Distributive Property...Only use this way if you have not learned the Distributive Property, since the numbers are more complex)

x+6 = 3(5-x) Divide each side by 3

[x+6]/3 = [3(5-x)]/3 [brackets were used for the numerators because fractions are difficult to show with this program]

x/3 + 6/3 = 5-x  OR  x/3 + 2 = 5-x 

Using 2 seperate steps, and in either order, pick whether to +x & -2 to each side (way 3) OR -x/3 & -5 from each side (way 4). The variables and constants end up on opposite sides with the 2 ways, but both are ok.

Way 3                                     Way 4

x/3 + 2 = 5-x     (+x & -2)        x/3 + 2 = 5-x     (-x/3 & -5)

4/3 x = 3  OR  4x/3 = 3            -3 = -4/3 x OR  -3 = -4x/3

Multiply by 3/4                        Multiply by -3/4

1x = 9/4  OR  x=9/4                 9/4 = 1x  OR  9/4 = x

(or 2.25 if you divide it to a decimal)

Answer 3

x+6=3(5-x)

Hi. I haven't worked with you before so I am going to break this down as simply as I can. Perhaps some of the things I say you will already know.

This is an equation since it has an equal sign and an expression on either side of the equal sign. The only variable (letter) which appears is x. So this is an equation in 1 variable.

The rule for solving equations for one variable is this: what you do to one side of the equation, you can do to the other. This means you can add, subtract, multiply or divide as much as you want as long as you do it to both sides of the equation. The exception is dividing by 0. You cannot do that.

The first step in this problem is to expand the terms on either side of the equation. There is nothing to do on the left side (x+6). On the right, you have 3(5-x) where the parentheses () mean multiplication. In this case, the 3 is being multiplied by everything inside the parentheses. We can expand this by multiplying that 3 by each thing inside, one at at time. 3(5-x) becomes 3*5 + 3 *(-x). This is 15-3x. Rewrite your equation with this on the right side.

x+6=15-3x

You want all of the x terms on one side of the equation and all of the numeric terms on the other side. It doesn't matter which way you move them, but after a while you will figure out which way saves a step or two.

I decide I want to move the -3x term over to the left side. How do I do this? Remember you can add, subtract, multiply or divide as much as you want as long as you do it to both sides of the equation.

I will add +3x to each side of the equation, and rewrite.

x+6+3x=15-3x+3x

Notice that the term +3x is now on each side. On the right, side, you can simplify, as -3x and +3x cancel out to make zero. Now we have

x+6+3x=15

On the left, we combine x and 3x to get:

4x+6=15

Now you want to move the numeric term to the other side of the equal sign. Move the 6 to the right side by subtracting 6 from both sides, (or by adding a negative six to each side).

4x+6-6=15-6

On the left side the +6 and the -6 cancel, leaving just 4x. On the right side, 15-6 becomes 9

Now you have 4x=9

Better, but not yet finished. You want to move that 4 over to the right side too. But since it is being multiplied by the x, you cannot cancel it out by adding or subtracting a number.

Instead, divide both sides by 4 and simplify

(4x)/4 = 9/4

On the left side, the division and multiplication of x by the same number cancel out to leave just X.

The final answer:
X = 9/4

I know I went into painful detail there, but I don't know at what point you are stuck on this problem. My goal isn't to give you the answer but rather to teach you how to solve it on your own. I hope this helps.