Keeping Track of Minus Signs in Parentheses: Subtraction

Algebra 1 Tutorial

Keeping Track of Minus Signs in Parentheses: Subtraction

Intro

When evaluating an expression, the operations inside parentheses must be performed first.
So 3 - (4-2) is the same as 3 - 2. Both are equal to 1. The correct treatment of plus and minus signs often causes confusion, especially when there are variables in the expression.

Sample Problem

You wish to solve the following equation for x.

6x - (4 - 2x) = 20

To do so you must “get rid” of the parentheses.

Solution

6x - (4 - 2x) = 20
On the left side of the equation we are subtracting a +4 and a -2x from 6x. Remember that subtracting a negative is the same as adding a positive.

So the left side becomes 6x - 4 + 2x ! In this case subtracting a negative 2x is the same as adding a positive 2x. Now we complete the problem.

6x - 4 + 2x = 20
8x - 4 = 20 ……..6(x’s) plus (2 x’s) equals 8(x’s)

8x - 4 + 4 = 20 + 4 ..adding 4 to both sides

8x = 24 ……cancelling + and – 4 from the left
…………….side and summing the right side

8x / 8 = 24 / 8 ……dividing both sides by 8
x = 3 ………………doing the division

CHECK
If x = 3
6x - (4 - 2x) = 20 becomes
6x3 -(4-3x3) ……substituting 3 for x
18 - (-2) ………doing the arithmetic
18 - (-2) =20 …..so we are right !



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