Shortcut for Solving Equations, A
Any term in an equation can be transferred to the other side if you change the sign. An explanation of this shortcut for solving equations.
Subject: term
Transcript: CHANGED THE SIGN. THIS IS A SHORTCUT. ANY TERM IN AN EQUATION CAN BE TRANSFERRED TO THE OTHER SIDE IF WE CHANGE THE SIGN. IN THE EQUATION 3X PLUS 5 EQUALS
Subtraction Problem
MM_ALG_03K_011
Subject: term
Transcript: WE BEGIN BY CHANGING SUBTRACTION TO ADDITION. NEXT, WE CHANGE THE SIGNS OF ALL THE TERMS IN PARENTHESES. 5XY BECOMES MINUS 5XY. AND MINUS 3Z BECOMES
Equation with Binomials in the Denominators, An
The solution to an equation with binomials in the denominators is detailed and checked.
Subject: term
Transcript: OVER X MINUS 12. THE X MINUS 12'S CANCEL, LEAVING X. NEXT, MULTIPLY THE SECOND TERM BY X MINUS 12. WE GET 3X MINUS 36. NOW LET'S MULTIPLY THE RIGHT SIDE
Equation with Rational Expressions: Practice Problem
A problem to practice solving a equations with a rational expression.
Subject: term
Transcript: . MULTIPLY THE FIRST TERM ON THE LEFT SIDE OF THE EQUATION. THAT'S 2X TIMES 6, OR 12X. WE ALSO HAVE 2X TIMES 3 OVER 2X. THE 2X'S CANCEL. THE RESULT IS 3. SO
Equation with No Solution, An
An equation with binomials in the denominators is solved. When the solution is checked, we find that it is not an allowable solution.
Subject: term
Transcript: THE RIGHT SIDE OF THE EQUATION. THE X MINUS 5'S CANCEL, LEAVING US WITH X. NOW WE'LL SOLVE THE EQUATION. COMBINE TERMS ON THE LEFT SIDE, THEN SUBTRACT 6
Example of Multiplying Both Equations
There is always more than one way to solve a system of equations with the elimination method. This example includes tips for deciding which term to
Subject: term
Transcript: X-TERMS HAVE OPPOSITE SIGNS. THAT MEANS WE WON'T HAVE TO CHANGE THE SIGNS OF THE TERMS IN ONE EQUATION WHEN WE MULTIPLY. THE X-TERMS ALSO HAVE SMALLER
Example of Solving Systems with Fractions
Solving another system of equations using multiplication and the least common denominator to find the solution.
Subject: term
Transcript: SAME BASIC STRATEGY WE'VE USED ALL ALONG, WE MULTIPLY THE EQUATIONS TO GET TERMS THAT ARE EASIER TO WORK WITH. LOOK AT THE FRACTIONS IN THE FIRST
Factor: x2 5x - 24
A quadratic trinomial in which the last term is negative is factored.
Subject: term
Transcript: HERE'S ANOTHER EXPRESSION WITH A NEGATIVE TERM. IN THIS CASE, THE LAST TERM IS NEGATIVE AND THE MIDDLE TERM IS POSITIVE. SO WE'LL WANT A PAIR OF
Factor: a2 - ac - ab bc
When grouping terms, the goal is to end up with an expression that is equal to the original polynomial. Close attention to the signs is necessary to
Subject: term
Transcript: SO FAR, EVERY TIME WE'VE FACTORED BY GROUPING WE'VE HAD A PLUS SIGN BETWEEN THE TWO GROUPS. A POSITIVE SIGN IN FRONT OF TERMS IN PARENTHESES DOESN
Variables and the Greatest Common Factor
To factor completely, the greatest common factor must include every number and variable that is a factor of each term in the polynomial. A
Subject: term
Transcript: SO FAR WE'VE FOUND THE GREATEST COMMON FACTOR BY WORKING WITH THE COEFFICIENTS OF TERMS. BUT VARIABLES CAN ALSO BE A PART OF THE GREATEST COMMON