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# 3(x-4)-5=-2+5x-9

Hi, Kathleen.  We are neighbors in PSL.

I hope the purpose you wanted to address this algebra question you posed has been resolved.  If not, feel free to contact me.  I usually like to meet in study rooms on the library with students.

Originally, you wrote:  3(x-4)-5=-2+5x-9.  The two tutors on September 6th addressed this equation.  It has numbers (integers) and a variable (x) on both sides of the equal sign.  Keeping a steady order of tackling this kind of work will benefit you.  So, first, on the left side of the equal sign, you'll want to separate out your term with the variable from the term without a variable.  Steven mentioned the use of the distribution problem.  The '3' on the outside of the paranthesis gets to be multiplied to both the 'x' and to the '4.'  You get to retain the '-' sign between the terms.  So, the left side becomes 3x - 12 - 5.

Then, we get to "combine like terms."  The 12 and the 5 do NOT have a variable attached to them, so it is OK to combine them.  How are you with addition/subtraction of negative numbers?  Are you allowed to use a calculator?  I know people studying for the TEAS need to be able to combine '-12' and '-5' without a calculator.  A good rule of thumb is that if the signs match, you add and then keep the sign.  For instance, both of these numbers are negative.  So, add together 12 and 5 to get 17.  As the numbers in the equation are negative, you then keep the minus sign in the equation.  So, we have simplified the left side of the equation to 3x - 17.

(Side note:  if the signs of two numbers you combine are different, then you treat with subtraction and keep the sign of the number with the largest absolute value.  If what I wrote scares you, think of this:  -5 + 12 would be solved '12-5 = 7;' the answer would be positive because 12 is farther from zero than -5.  If the question instead was -12 + 5, then you would still think 12-5.  The answer, though, would be -7 because -12 is farther from zero than 5.)

Take care!  I hope you are doing well.

The first thing you will need to do is distribute so you would get 3x-12-5=2+5x-9 I personally like to have everything in the same order so I would write it as 3x-12-5= 5x+2-9 The next thing you want to do is combine like terms on each side of the equation

3x-17=5x-7 Now you want the x's to one side so

3x-3x-17=5x-3x-7 which gives you -17=2x-7

Then you need to move your constants to one side

-17+7= 2x-7+7 which gives you -10=2x

Now divide both sides by 2 to solve for x

-10/2=2x/2

-5=x