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Writing a Rational Expression in Lowest Terms
Solving Quadratic Inequalities with a Sign Graph
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The Square of a Binomial
Properties of Negative Exponents
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Simple Trinomials as Products of Binomials
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Multiplying and Dividing Fractions 2
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Solving Nonlinear Equations by Substitution
The Distance and Midpoint Formulas
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Graphing Using x- and y- Intercepts
Properties of Exponents
Solving Quadratic Equations
Solving One-Step Equations Using Algebra
Relatively Prime Numbers
Solving a Quadratic Inequality with Two Solutions
Operations on Radicals
Factoring a Difference of Two Squares
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Solving Quadratic Equations by Factoring
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Simplifying Expressions Involving Variables
Adding Integers
Factoring Completely General Quadratic Trinomials
Using Patterns to Multiply Two Binomials
Adding and Subtracting Rational Expressions With Unlike Denominators
Rational Exponents
Horizontal and Vertical Lines

Calculations with Negative Numbers

Question: What is the value that satisfies -4 + ? = -10 ?


There are several possible misconceptions including

? = 6


? = 14

or even

? = - 14


The correct answer is - 6 as this satisfies the sum -4 + (-6) = -10. It can be shown on a number line as given below.

Starting at negative 4 and adding negative 6 you get the answer negative 10.

Hence -4 + (-6) = -10.

Further Explanation

It is important to realise that there is no guessing, no doubts but straightforward logic. Here we can associate the meaning owning when the quantity is positive and owing if it negative. Also, as before, we associate the minus sign with opposite.

In this example,

I start by owing 4 ( i.e. the '- 4 ' )

What is this '+?' that must have happened if I ended up 'owing 10' ? ( i.e. the ' - 10 ')

Another debt of 6 must have been added to my plight

We write 'adding a debt of 6' as ' + ( -6) '

So in - 4 + ? = - 10 the ? must be - 6

This is equivalent to the use of a number line as shown above; it does not matter which way you argue as long as you get the logic correct!

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