How do you solve #3(x-7) = 6(x-10)#?

Question

Julia Adams · Accepted Answer

#x = 13#

#3(x-7) = 6(x-10)#

Use the distributive property (shown below) to simplify each side:

Following this image, we know that:
#color(blue)(3(x-7) = (3 * x) + (3 * -7) = 3x - 21)#
and
#color(blue)(6(x-10) = (6 * x) + (6 * -10) = 6x - 60)#

Put them back into the equation:
#3x - 21 = 6x - 60#

Subtract #color(blue)6x# from both sides:
#3x - 21 quadcolor(blue)(-quad6x) = 6x - 60 quadcolor(blue)(-quad6x)#

#-3x - 21 = -60#

Add #color(blue)21# on both sides:
#-3x - 21 quadcolor(blue)(+quad21) = -60 quadcolor(blue)(+quad21)#

#-3x = -39#

Divide both sides by #color(blue)(-3)#:
#(-3x)/color(blue)(-3) = (-39)/color(blue)(-3)#

Therefore,
#x = 13#

Hope this helps!

Eva Abramson · Answer

#x=13#

We can divide both sides by #3# to get

#x-7=2(x-10)#

Next, we can distribute the #2# on the right to get

#x-7=2x-20#

Next, we can add #7# to both sides to get

#x=2x-13#

To get our constants on one side, we can subtract #2x# from both sides to get

#-x=-13#

Lastly, we can divide both sides by #-1# to get

#x=13#

Hope this helps!

Jameson Allen · Answer

undefined First, distribute the 3 and the 6 across the parentheses to get 3x - 21 = 6x - 60. Then, move all the x terms to one side and constants to the other side. You get 3x - 6x = -60 + 21. Combine like terms to get -3x = -39. Finally, divide both sides by -3 to solve for x, which gives x = 13.

Eva Abramson · Answer

undefined To solve $ 3(x-7) = 6(x-10) $, you would follow these steps:

1. Distribute the constants outside the parentheses:
$$ 3x - 21 = 6x - 60 $$

2. Rearrange the equation by moving like terms to the same side of the equation:
$$ 3x - 6x = -60 + 21 $$

3. Combine like terms:
$$ -3x = -39 $$

4. Divide both sides by the coefficient of $ x $ to solve for $ x $:
$$ x = \frac{-39}{-3} $$

5. Simplify the fraction:
$$ x = 13 $$

So, the solution to the equation is $ x = 13 $.