Question

Imagine you are teaching a fellow student how to solve:
3 − 5(x + 2) = 3(x + 1) + 6

In your own words, explain the process for solving this equation. Please include your work at each step of the process along with the final answer.

Answer 1

Ask the student(s) to separate both halves of the equation, and treat them as individual equations on their own and set them to equal y. Thus giving;

y = 3 - 5(x+2)
y = 3(x+1) + 6.

My next step would be to ask the student to expand both sets of brackets in said equations remembering to look carefully at the positivity or negativity of the bracket coefficient i.e -5(x+2) = -5x-10.

The expansion of the brackets would give;

y = 3 - 5x - 10 and,
y = 3x + 3 + 6

Next step would be to simplify both equations giving,

y = -5x - 7 and,
y = 3x + 9

Then because you've set both equations to = y, you can put them both back together as one creating the master equation (^_^) of;

3x + 9 = -5x - 7

Next, ask the student to simplify that equation by getting x on it's own on one side i.e. +5x to both sides of the equation giving;

8x + 9 = -7

Then the student should -9 from both sides of the equation to get rid of the +9 (What you do to one side must be replicated on the other) leaving them with;

8x = -16

Finally, divide each side by 8 which gives you;

x = -2.

Hope this helped :)