Evaluating Variable Expressions with Integers

Evaluating Variable Expressions with Integers

Remember that to evaluate an expression means to substitute a number for the variable in the expression. Now we can use negative numbers as well as positive numbers when evaluating expressions.

Example

Evaluate \(x+7\phantom{\rule{0.2em}{0ex}}\text{when}\phantom{\rule{0.2em}{0ex}}\)

  1. \(\phantom{\rule{0.2em}{0ex}}x=-2\phantom{\rule{0.2em}{0ex}}\)
  2. \(\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}x=-11.\)

Solution

Evaluate \(x+7\) when \(x=-2\) 
 Evaluating Variable Expressions with Integers
Evaluating Variable Expressions with IntegersEvaluating Variable Expressions with Integers
Simplify.Evaluating Variable Expressions with Integers
Evaluate \(x+7\) when \(x=-11\) 
 Evaluating Variable Expressions with Integers
Evaluating Variable Expressions with IntegersEvaluating Variable Expressions with Integers
Simplify.Evaluating Variable Expressions with Integers

Example

When \(n=-5,\) evaluate \(\)

  1. \(\phantom{\rule{0.2em}{0ex}}n+1\phantom{\rule{0.2em}{0ex}}\)
  2. \(\phantom{\rule{0.2em}{0ex}}-n+1.\)

Solution

Evaluate \(n+1\) when \(n=-5\) 
 Evaluating Variable Expressions with Integers
Evaluating Variable Expressions with IntegersEvaluating Variable Expressions with Integers
Simplify.Evaluating Variable Expressions with Integers
Evaluate \(-n+1\) when \(n=-5\) 
 Evaluating Variable Expressions with Integers
Evaluating Variable Expressions with IntegersEvaluating Variable Expressions with Integers
Simplify.Evaluating Variable Expressions with Integers
Add.Evaluating Variable Expressions with Integers

Next we’ll evaluate an expression with two variables.

 

Example

Evaluate \(3a+b\) when \(a=12\) and \(b=-30.\)

Solution

 Evaluating Variable Expressions with Integers
Evaluating Variable Expressions with IntegersEvaluating Variable Expressions with Integers
Multiply.Evaluating Variable Expressions with Integers
Add.Evaluating Variable Expressions with Integers

Example

Evaluate \({\left(x+y\right)}^{2}\) when \(x=-18\) and \(y=24.\)

Solution

This expression has two variables. Substitute \(-18\) for \(x\) and \(24\) for \(y.\)

 \({\left(x+y\right)}^{2}\)
Evaluating Variable Expressions with Integers\({\left(-18+24\right)}^{2}\)
Add inside the parentheses.\({\left(6\right)}^{2}\)
Simplify\(36\)

Optional Video: Example on Adding Integers by Mathispower4u

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This is a lesson from the tutorial, Introducing Integers and you are encouraged to log in or register, so that you can track your progress.

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