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How do I solve this equation: 5(x+3)-(4x-6)=-4

Help please!  I have substituted 25, 17, 13 and -25 from the answer bank - none of which balance out to a -4.  Completely stumped.

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Brad M. | STEM Specialist plus Business, Accounting, Investment & EditingSTEM Specialist plus Business, Accountin...
4.9 4.9 (233 lesson ratings) (233)
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Hey Janie -- sometimes the formula "looks better" by "putting the negative element on the other side":

5 (x + 3) - (4x - 6) = -4 ... 5(x +3) = (4x -6) -4 ... 5x +15 = 4x -10 ... notice a positive "x" cannot work -- the "5x" side would always "outrun" the "4x" side ... only the -25  makes sense ... Best wishes, ma'am :)

Mike C. | Enthusiastic Tutor for Middle and High School StudentsEnthusiastic Tutor for Middle and High S...
4.8 4.8 (82 lesson ratings) (82)
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Hello Janie.

Since you didn't get the right answer by taking answers out of the bank, let's try a solution method that doesn't involve guess-and-check.

5 (x + 3) - (4x - 6) = -4;
5x + 15 - 4x + 6 = -4;

x + 21 = -4;

x = -25.

So your not finding an answer is probably due to errors after plugging in x = -25. Let's try it again:

5 (-25 + 3) - (4(-25) - 6) = -4;

5 (-22) - (-100 - 6) = -4;

-110 - (-106) = -4;

-110 + 106 = -4;

-4 = -4.

Dan M. | Math, Physics and Chemistry TutorMath, Physics and Chemistry Tutor
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Janie, I agree with Raffi on his approach and technique in solving the problem. When you tried to check for

x=-25 and did not get it to balance, it is likely that you erred when you distributed the negative sign through the second term. See how your math compares to this:

if x=-25 then  5(x+3)-(4x-6)=-4   becomes     5( -25+3) - ( 4( -25) -6) = -4

                                                                         5( -22) - ( -100 -6) = -4

                                                                                -110 - ( -106) = -4

                                                                                    -110 + 106 = -4

                                                                                                 -4 = -4

If your difficulty was in distributing the negative sign through that second term, I would encourage you to practice some more problems with that feature! good luck

Raffi H. | Experienced and Successful Tutor and Former TeacherExperienced and Successful Tutor and For...
4.9 4.9 (695 lesson ratings) (695)
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Hi Janie. I hope this helps....

Start by distributing the 5 over the (x-3) to get

5x + 15 -(4x-6) = -4

Now distribute the -1 in front of the (4x-6) over the two terms in parentheses to get

5x + 15 -4x + 6 = -4 (the 6 is now positive b/c -1 x -6 is pos 6)

Comine terms with that contain x; combine numbers to get

x + 21 = -4

Now subtract 21 from both sides to get

x = -25

Best wishes.

Raffi