Solving Linear Equations Practice

1. Solve for $c$.

   Give an exact answer.

   $0.2(10-5c)=5c-16$

2. Solve for $e$.

   Give an exact answer.

   $0.75(8+e)=2-1.25e$

3. Solve for $m$.

   Give an exact answer.

   $4(1+0.5m)=7m$

4. Solve for $d$.

   Give an exact answer.

   $0.5(7d+4)=7-1.5d$

Source: Khan Academy, https://www.khanacademy.org/math/college-algebra/xa5dd2923c88e7aa8:linear-equations-and-inequalities/xa5dd2923c88e7aa8:solving-equations-with-one-unknown/e/multi-step-equations-rational
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1. We need to manipulate the equation to get ‍$c$ by itself.

   $0.2(10-5c) = 5c-16$
   $2-c = 5c-16$	Distribute
   $2-c {-5c} = 5c-16 {-5c}$	Subtract $5c$ from each side
   $2-6c = -16$	Combine like terms
   $2-6c {-2} = -16 {-2}$	Subtract 2 from each side
   $-6c =-18$	Combine like terms
   $\dfrac{-6c}{ {-6}} = \dfrac{-18}{ {-6}}$	Divide each side by -6
   $c = {3}$	Simplify

   The answer: $c = { 3 }$

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2. We need to manipulate the equation to get ‍$e$ by itself.

   $0.75(8+e)=2-1.25e$
   $6+0.75e=2-1.25e$	Distribute
   $6+0.75e{+1.25e} = 2-1.25e{+1.25e}$	Add $1.25e$ to each side
   $6+2e =2$	Combine like terms
   $6+2e -6 =2 -6$	Subtract 6 from each side
   $2e = -4$	Combine like terms
   $\dfrac{2e}{{2}} = \dfrac{-4}{{2}}$	Divide each side by 2
   $e = {-2}$	Simplify

   
   The answer: $e = {-2}$

   ---

3. We need to manipulate the equation to get ‍$m$ by itself.

   $4(1+0.5m)=7m$
   $4+2m = 7m$	Distribute
   $4+2m{-2m} = 7m{-2m}$	Subtract $2m$ from each side
   $4 =5m$	Combine like terms
   $2-6c {-2} = -16 {-2}$	Subtract 2 from each side
   $-6c =-18$	Combine like terms
   $\dfrac{4}{{5}} = \dfrac{5m}{{5}}$	Divide each side by 5
   $m = {0.8}$	Simplify

   
   The answer: $m = {0.8}$

   ---

4. We need to manipulate the equation to get ‍$d$ by itself.

   $0.5(7d+4)=7-1.5d$
   $3.5d+2 = 7-1.5d$	Distribute
   $3.5d+2{+1.5d} = 7-1.5d{+1.5d}$	Add $1.5d$ to each side
   $5d =5$	Combine like terms
   $5d+2{-2} = 7{-2}$	Subtract 2 from each side
   $2e = -4$	Combine like terms
   $\dfrac{5d}{{5}} = \dfrac{5}{{5}}$	Divide each side by 5
   $d = {1}$	Simplify

   
   The answer: $d = {1}$