Question

3x
Are 10 - 20 and 5(2 - 20) equivalent expressions? Explain.

Answer 1

`\huge\text{Hey there!}`

`\large\text{\bold{No, they are not equivalent because...}}\\\\\\\large\textsf{5(2 - 20)}\\\large\textsf{= 5(2) + 5(-20)}\\\large\textsf{= 10 - 90}\\\boxed{\large\textsf{= \bf -90}}\\\\\large\textsf{10 - 20}\\\large\textsf{\boxed{\large\textsf{= \bf -10}}}\\\\\\\large\boxed{\star}\large\textsf{-10}\\eq\large\textsf{-90}\large\boxed{\star}`

`\huge\boxed{\mathsf{Answer: \bold{NO,}\ because \ \bf -10 \ does \ NOT}}\\\huge\boxed{\mathsf{\bf equal \ to -90}}\huge\checkmark`

`\bullet\ \frak{Random\ fact: negatives \ are \ on\ the\bf \ LEFT\ side\ of\ the \ number\ line\ \& \ positives}\\\frak{are\ on\ the\bf \ RIGHT\ side\ of\ the\ number\ line}`

`\large\text{Good luck on your assignment \& enjoy your day!}\\\\\\\huge\boxed{\frak{Amphitrite1040}}`

Answer 2

No.

Explanation:

Take the second expression: 5(2 - 20)

To solve, you must distribute the 5 to all terms within the parenthesis:

5(2 - 20) = (5 * 2) - (5 * 20) = 10 - 100 = -90

On the other hand:

10 - 20 = -10

∴ the two expressions are not equivalent.