Tip:
Highlight text to annotate it
X
- WE WANT TO SOLVE THE FOLLOWING MULTI-STEP LINEAR EQUATION
AND I HAVE THE STEPS DOWN HERE IN RED IF NEEDED.
THE IMPORTANT THING TO REMEMBER IS,
THE GOAL IS TO ISOLATE THE VARIABLE
ON ONE SIDE OF THE EQUATION OR ONE SIDE OF THE EQUAL SIGN.
SO LOOKING AT OUR EQUATION HERE,
THE FIRST STEP IS GOING TO BE TO CLEAR THE PARENTHESES,
AND WE CAN DO THIS BY DISTRIBUTING.
SO WE'LL DISTRIBUTE HERE AND HERE,
AS WELL AS HERE AND HERE.
WE NEED TO BE CAREFUL HERE BECAUSE OF THE MINUS SIGN HERE.
WE WOULD HAVE 2 - 5 x X, SO I'LL HAVE - 5X,
AND THEN - 5 x 5, WHICH IS 25.
AND THIS WOULD BE EQUAL TO 3 x X, OR 3X - 3 x 2,
SO I'LL HAVE - 6 AND THEN - 1.
NOW BEFORE WE GO ANY FURTHER, WE SHOULD COMBINE LIKE TERMS
ON THE LEFT SIDE OF THE EQUATION
AND THE RIGHT SIDE OF THE EQUATION.
NOTICE HOW WE CAN COMBINE THESE TWO TERMS
AS WELL AS THESE TWO TERMS.
2 - 25 WOULD BE -23,
SO WE'LL HAVE -23 - 5X = HERE WE'LL HAVE 3X
AND THEN WE CAN THINK OF THIS AS -6 - 1.
THAT'D BE -7
AND THEN INSTEAD OF WRITING +-7, IT'S MORE COMMON TO WRITE -+7.
REMEMBER THOSE WOULD BE EQUIVALENT.
NOW NOTICE ON THIS EQUATION WE HAVE VARIABLE TERMS
ON BOTH SIDES OF THE EQUATION.
IF OUR GOAL IS TO ISOLATE THE VARIABLE ON ONE SIDE,
WE NEED TO ADD OR SUBTRACT
TO ELIMNATE ONE OF THE VARIABLE TERMS ON EITHER SIDE.
SO WE WANT TO ELIMINATE THE - 5X ON THE LEFT.
WE CAN ADD 5X TO BOTH SIDES
OR IF WE WANT TO ELIMINATE THIS +3X,
WE COULD SUBTRACT 3X ON BOTH SIDES.
IT SEEMS MOST PREFERRED TO HAVE THE VARIABLE TERMS
ON THE LEFT SIDE,
SO WE'LL UNDO THIS +3X BY SUBTRACTING 3X
ON BOTH SIDES OF THE EQUATION.
SO WE'D HAVE -23 AND THEN - 5X - 3X, OR -5X - 3X,
THAT WOULD BE -8X.
SO I'LL WRITE - 8X MUST EQUAL 3X, - 3X, THAT'S 0.
THAT'S WHY WE DID THAT.
AND THEN WE HAVE -7.
AND NOW WE FINALLY HAVE A BASIC TWO-STEP EQUATION.
WE WANT TO UNDO THIS -23
AS WELL AS UNDO THIS MULTIPLICATION HERE.
WELL WE CAN UNDO -23 BY ADDING +23.
SO IF WE ADD 23 TO BOTH SIDES OF THE EQUATION,
NOTICE THIS WOULD BE 0,
BUT WE MUST ALSO DO THE SAME TO THE OTHER SIDE,
SO THIS WOULD BE 0.
BRING DOWN THE -8X.
AND HERE WE HAVE -7 + 23, WHICH WOULD BE + 16.
AND THEN THE LAST STEP, BECAUSE -8X MEANS -8 x X,
WE'RE GOING TO DIVIDE BOTH SIDES BY -8.
SO AT -8 DIVIDED BY -8 WOULD BE +1 x X WHICH IS X.
AND ON THE RIGHT SIDE WE HAVE +16 DIVIDED BY -8,
WHICH IS EQUAL TO -2.
SO OUR SOLUTION IS X = -2.
WE WON'T TAKE THE TIME TO CHECK THIS SOLUTION,
BUT WHAT THAT MEANS IS, IF WE SUBSTITUTE -2 FOR X
IN THE ORIGINAL EQUATION,
IT WOULD MAKE THIS EQUATION TRUE
WHERE IT WOULD SATISFY THIS EQUATION.
SO YOU MAY WANT TO TAKE A MOMENT AND VERIFY THAT.
I HOPE THIS WAS HELPFUL.