Rose Harrison and Clara Huizink Solutions for Exercise 5: Practice 1

Solve the equation $-(x+2)-3x=2(x+1)$. Show the equivalence transformation that used at each step and check the solution. (Write the answer in fraction.)

Find the value of $x$ for the equation $1-3(x+2)=\frac{1}{2}(2x-8)+3$ using the equivalence transformation.

Find the value of $x$ for the equation $\frac{x}{3}+2=\frac{1}{2}x-4$.

Find the value of $x$ for the equation $\frac{x+2}{5}=\frac{2x-4}{2}$ using the equivalence transformation.

Solve the equation $\frac{1}{3}(6x-3)=\frac{1}{4}(8-4x)$. Show the equivalence transformation that used at each step and check the solution. 

Solve the equation $2x=\frac{1}{5}(9-8x)$. Show the equivalence transformation that used at each step and check the solution. (Write the answer in fraction.)

For the equation $x=3$, use equivalence transformations to write an equivalent equation with brackets and the variable $x$ on both sides of the equal sign.

Apply equivalence transformations to the equation $5(x+4)-8+x=6(x+2)$. Describe what happens, and explain what you think this means.