How do you solve #-(3k-12)=48# using the distributive property?

Question

Hazel Anglin · Accepted Answer

#k = -12#

We first simplify the left hand side using the distributive property, shown here:

Following this image, the left hand side of the equation would become:
#-1 * 3k - 1 * -12#

#-3k + 12#

Putting this back into the equation:
#-3k + 12 = 48#

Now, subtract #color(blue)12# from both sides of the equation:
#-3k + 12 quadcolor(blue)(-quad12) = 48 quadcolor(blue)(-quad12)#

#-3k = 36#

Divide both sides by #color(blue)(-3)#:
#(-3k)/color(blue)(-3) = 36/color(blue)(-3)#:

So:
#k = -12#

Hope this helps!

Eva Abramson · Answer

undefined To solve the equation $-(3k - 12) = 48$ using the distributive property, follow these steps:

1. Apply the distributive property to remove the parentheses. In this case, distribute the negative sign (which is the same as multiplying by -1) across each term inside the parentheses:
   $-1 \times 3k + (-1) \times (-12) = 48$
   $-3k + 12 = 48$

2. Next, isolate the variable term ($-3k$) by moving the constant term to the other side of the equation. You can do this by subtracting 12 from both sides:
   $-3k + 12 - 12 = 48 - 12$
   $-3k = 36$

3. Finally, solve for $k$ by dividing both sides of the equation by -3:
   $-3k / (-3) = 36 / (-3)$
   $k = -12$

Therefore, the solution to the equation $-(3k-12)=48$ is $k = -12$.