Question

How do you solve the equations: -(1+4m)-6m=-81 and 238=-5(6v-7)-7

Answer 1

-(1+4m)-6m=-81
 -1-4m-6m=-81
-1-10m=-81
+1          +1
-10m=-80
---------------
-10
m=8

--------------------
238=-5(6v-7)-7
238=-30v+35-7
238=-30v+28
-28            -28
210=-30v
---------------
-30
v=7

Answer 2

To solve an equation, we need to isolate the variable and simplify out other terms. In these equations, we will use the distributive property.

-(1+4m)-6m=-81     We start with our equation.
-1-4m-6m=-81     We distribute our "-."
-1-10m=-81     We combine our like-terms.
+1           +1
-10m=-80     We add1 to both sides (to isolate the variable).
/-10    /-10
m=8     We divide by -10 on both sides (to isolate the variable).

With the math above, we know that the solution to the first equation is that m=8. Now let's begin the second.

-5(6v-7)-7=238     We start with our equation.
-30v+35-7=238     We distribute our "-5."
-30v+28=238     We combine our like-terms.
        -28   -28
-30v=210     We subtract 28 from both sides (to isolate the variable).
/-30   /-30
v=-7     We divide by -30 on both sides (to isolate the variable).7

Using the math above, we can see that the solution to the second equation is v=-7.