2. Solve for   x   and check.   2(x - 1) + 4 = 3x - (2x - 3)

Let us follow the steps for solving first degree equation

  1. Clear denominators.
  2. Simplify. Remove parentheses and combine like terms.
  3. Transpose known terms to one side and unknown terms to the other.
  4. Combine.
  5. Divide both sides by the coefficient of the unknown.
  6. Check.

There are no denominators to clear, so we move on to remove parentheses and comvine like terms.

Remove parentheseses

2x - 2 + 4 = 3x - 2x + 3

Combine like terms

2x + 2 = x + 3

Transpose

2x - x = 3 - 2

Combine

x = 1

and there is nothing to do at step 5. We are done.   x = 1.

Check. Copy down the original equation except that where you see the unknown, copy down what the unknown is equal to in parentheses.

2(x - 1) + 4 = 3x - (2x - 3)

2((1) - 1) + 4 = 3(1) - (2(1) - 3)

This gives us an order of operations problem. Do what's inside parentheses first. The parentheses pn the right side have a product and a difference. Do the product first

2(1 - 1) + 4 = 3(1) - (2 - 3)

Then do the differences inside the parentheses

2(0) + 4 = 3(1) - (-1)

Now do the products

0 + 4 = 3 - (-1)

then the sums and differences.

4 = 4

and it checks.