Question 842061

Problem 1.) Ten less than the product of x and 9 is 8.


Problem 2.) Twice the difference of a number and 3 is the same as 1 added to three times the number. Find the number.


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Problem 1.) Ten less than the product of x and 9 is 8.


Step 1.) Interpret the words.


Ten less than(-10) the product(multiplication) of x and 9 is(=) 8.

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Problem 1.)


Step 2.) Put equation together.


{{{9x-10=8}}}

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Problem 1.)

Step 3.) Solve for "x".


{{{9x-10=8}}}


{{{9x-10+10=8+10}}}


{{{9x=18}}}


{{{9x/9=18/9}}}


{{{x=2}}}


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Problem 1.)

Step 4.) Check using {{{x=2}}}.


{{{9x-10=8}}}

{{{9(2)-10=8}}}

{{{18-10=8}}}

{{{8=8}}}


Checks!

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Problem 1.)

Step 5.) Answer.

{{{x=2}}}


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Problem 2.) Twice the difference of a number and 3 is the same as 1 added to three times the number. Find the number.



Step 1.) Interpret the words.


Twice(multiply by 2) the difference(-) of a number(x) and 3 is(=) the same as 1 added(+) to three times the number(3x). Find the number.


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Problem 2.)

Step 2.) Put equation together.

{{{2(x-3)=3x+1}}}

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Problem 2.)

Step 3.) Solve for "x".


{{{2(x-3)=3x+1}}}

{{{2x-6=3x+1}}}

{{{2x-2x-6=3x-2x+1}}}

{{{-6=x+1}}}

{{{-6-1=x+1-1}}}

{{{-7=x}}}

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Problem 2.)

Step 4.) Check using {{{x=-7}}}.

{{{2(x-3)=3x+1}}}

{{{2((-7)-3)=3(-7)+1}}}

{{{-14-6=-21+1}}}

{{{-20=-20}}}


Checks!


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Problem 2.)

Step 5.) Answer.

{{{x=-7}}}