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How do you solve #2x+3=3x-4#?

Answer 1

Genesis Allen

With practice you can do these quicker as you learn the shortcut.

#x=7#

Objective is to have a single #x# on one side of the = and everything else on the other side.

Given:#" "color(green)(2x+3=3x-4)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Step 1 ")color(brown)("Having all the "x" terms on one side of =")#

Subtract #color(red)(2x)# from both sides

#color(green)(2xcolor(red)(-2x)+3=3xcolor(red)(-2x)-4)#

#0+3=x-4#

Swap round

#x-4=3# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Step 2 ")color(brown)("Have just "x" on the left of =")#

Add #color(red)(4)# to both sides

#color(green)(x-4color(red)(+4)=3color(red)(+4))#

#x=7#

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Answer 2

Abigail Allen

To solve the equation 2x + 3 = 3x - 4, you need to isolate the variable x.

Step 1: Move all terms containing x to one side of the equation and constants to the other side. Subtract 2x from both sides: 2x - 2x + 3 = 3x - 2x - 4 3 = x - 4

Step 2: Add 4 to both sides: 3 + 4 = x - 4 + 4 7 = x

So, the solution to the equation is x = 7.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.