Solve the equation 3r+5=14.

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ishpiro's profile pic

ishpiro | College Teacher | (Level 1) Educator

Posted on

To solve the equation 3r + 5 = 14,

first, subtract 5 from both sides:

3r = 14 - 5

3r = 9

Then, divide both sides by 3:

r = 3

The solution of the equation is r = 3.

You can check this by substituting r = 3 back into the equation:

3r + 5 = 3*3 + 5 = 9 + 5 = 14.

Right side equals the left side when r = 3, so this is the correct solution.

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bababeta | Middle School Teacher | (Level 1) Adjunct Educator

Posted on

To solve the equation you need to balance both sides:

3r +5 =14

To find r we will use the inverse function machine

r -->x3 --> +5 --> 14

 3<--÷3 <-- -5<-- 14

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klaydyer | College Teacher | (Level 1) Adjunct Educator

Posted on

Algebra is about getting numbers to one side of the equation, and letters to the other. You accomplish this by working to isolate the letters thusly:

3R+5=14 means that in order to remove the 5 from the letter side, you subtract 5 thusly

3R+5-5

which creates 3R (the 5-5 cancels out to zero, and can be erased from the letter side)

but whatever to do to one side of an equation, you also have to do to the other so you now have to subtract 5 from the number side

14-5= 9

which gives you

3R=9

To remove the 3 from the letter side, you divide by the number in front of the letter, in this case 3. Again, remember that what you do to one side of the equation, you have to do to the other.

3R/3 = 9/3

Now simply finish off the basic math, and you get

R=3

Finally, double check your answer by inserting it back into your original equation:

3(3)+5=14

If this is correct (which it is), then you R value has to be correct.

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csmalley | eNotes Newbie

Posted on

Algebra is all about getting letters on one side and numbers on the other

So 3r + 5 = 14

3r = 14 minus 5 (when numbers change sides they change signs so add becomes minus)

3r = 9

then 9/ 3 (as it was multiplied against r so it changes and becomes divide)

R = 3

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olivera | eNotes Newbie

Posted on

The goal in this problem is to "isolate the variable" basically, get the letter, r, by itself on one side of the equals sign. In order to do that you have to work the order of operations (PEMDAS) backwards while making sure that the equation remains balanced. You're simply going to perform the opposite operation on each side of the equal sign until each side of the equal sign has only one letter or one number. 

3r+5=14 step 1: subtract 5 from each side. *remeber, you're subtracting because it is the opposite operation 

3r +5-5= 14-5

(5-5 =0 so the 5s cancel on the left side of the equal sign, leaving only the 3r remaining on that side  14-5=9)

3r=9 step 2: divide both sides of the equal sign by 3 since division is the opposite function in this case 

3r/3=9/3 

3/3=1 which leaves you with 1r (which is the same as simply "r"), 9/3=3

r=3

teachingisawsome's profile pic

teachingisawsome | (Level 1) eNoter

Posted on

The purpose of this problem is to get "r" alone on the left side of the problem. The right side of the equal sign should tell us what "r" equals.

Remember! What you do on one side, you MUST do to the other side. When you subtract 5 from the right side, you MUST subtract 5 from the other side. When you divide the right side by three, you MUST divide the left side by three.

3r+5=14

3r+5-5=14-5          subtract five from both sides

3r=9                    

3r/3 = 9/3              Divide both sides by three. 

r=3

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dkoprowski | eNotes Newbie

Posted on

You need to get the variable r by itself. To do this first we must get rid of the 5 by doing the inverse operation. We will subtract 5 from both sides of the equation so we are left with 3r=9. Then we must get rid of the 3 by doing the inverse. We divide by 3 on both sides so r=3. 

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glendadh | eNotes Newbie

Posted on

First you need to balance the equation.

3r +5 = 14

so to do this you would subtract 5 from both sides which leaves you with

3r = 9

then divide each side by 3 leaving you with

r = 3

mcshean's profile pic

Nolan McShea | Student, Grade 11 | (Level 2) Honors

Posted on

Hi there! Algebra may seem tricky at first, but you can see that it is just using the four mathematical operations of adding, subtracting, multiplying, and dividing. 

Check the image for the full solution and explanation I made!

Hope I helped!

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