Felicia is solving the expression -5(3x+2)+10x. Gregory is solving the expression -12-4x+?+?x. Both students simplified their answers to get the same expression. What are the values missing from Gregory's expression?

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calculista calculista · Answer 1 · 2020-03-16T15:13:56+01:00

Answer:

see the explanation

Step-by-step explanation:

we have

Felicia

[tex]-5(3x+2)+10x[/tex]

Apply distributive property

[tex]-5(3x)-5(2)+10x[/tex]

[tex]-15x-10+10x[/tex]

Combine like terms

[tex]-5x-10[/tex]

Let

a ----> the missing term with coefficient x in Gregory's expression

b ----> the missing constant term in Gregory's expression

so

[tex]-12-4x+ax+b[/tex]

equate Gregory's expression to Felicia's expression

[tex]-12-4x+ax+b=-5x-10[/tex]

so

[tex]-12+b=-10[/tex] ----->[tex]b=2[/tex]

[tex]-4x+ax=-5x[/tex] ------> [tex]a=-1[/tex]

so

Gregory's expression is

[tex]-12-4x+2-x[/tex]

therefore

The missing terms are 2 and -x