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2.7.7: Solving Linear Equations and Inequalities
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/02%3A_Vectors_and_Math_Review_Topics/2.07%3A_Math_Review_of_Other_Topics/2.7.07%3A_Solving_Linear_Equations_and_Inequalities
\[\begin{array} { l l } { \textbf { Subtraction Property of Inequality } } & { \textbf { Addition Property of Inequality } } \\ { \text { For any numbers } a , b , \text { and } c , } & { \text { For ...\[\begin{array} { l l } { \textbf { Subtraction Property of Inequality } } & { \textbf { Addition Property of Inequality } } \\ { \text { For any numbers } a , b , \text { and } c , } & { \text { For any numbers } a , b , \text { and } c } \\ { \text { if }\qquad \quad a < b } & { \text { if } \qquad \quad a < b } \\ { \text { then } a - c < b - c . } & { \text { then } a + c < b + c } \\\\ { \text { if } \qquad \quad a > b } & { \text { if } \qquad \quad a > b } \\ { \text { then } a - c > b -…
2.7.8: Solving Quadratic Equations
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/02%3A_Vectors_and_Math_Review_Topics/2.07%3A_Math_Review_of_Other_Topics/2.7.08%3A_Solving_Quadratic_Equations
At first glance, this one doesn’t look like a quadratic equation, but as we begin isolating x, as we always strive to do in solving for x, (hey, once we have x all by itself on the left side of the eq...At first glance, this one doesn’t look like a quadratic equation, but as we begin isolating x, as we always strive to do in solving for x, (hey, once we have x all by itself on the left side of the equation, with no x on the right side of the equation, we have indeed solved for x—that’s what it means to solve for x) we quickly find that it is a quadratic equation.
2.7.2: Solving Inequalities
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Introductory_Physics_II_(1112)/02%3A_Math_Review/2.07%3A_Solving_Linear_Equations_and_Inequalities/2.7.02%3A_Solving_Inequalities
\[\begin{array} { l l } { \textbf { Subtraction Property of Inequality } } & { \textbf { Addition Property of Inequality } } \\ { \text { For any numbers } a , b , \text { and } c , } & { \text { For ...\[\begin{array} { l l } { \textbf { Subtraction Property of Inequality } } & { \textbf { Addition Property of Inequality } } \\ { \text { For any numbers } a , b , \text { and } c , } & { \text { For any numbers } a , b , \text { and } c } \\ { \text { if }\qquad \quad a < b } & { \text { if } \qquad \quad a < b } \\ { \text { then } a - c < b - c . } & { \text { then } a + c < b + c } \\\\ { \text { if } \qquad \quad a > b } & { \text { if } \qquad \quad a > b } \\ { \text { then } a - c > b -…
2.7.3: Solving Quadratic Equations
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Introductory_Physics_II_(1112)/02%3A_Math_Review/2.07%3A_Solving_Linear_Equations_and_Inequalities/2.7.03%3A_Solving_Quadratic_Equations
The solutions to a quadratic equation of the form $a x^{2}+b x+c=0$ , where $a≠0$ are given by the formula: To use the Quadratic Formula, we substitute the values of $a,b$ , and $c$ from the sta...The solutions to a quadratic equation of the form $a x^{2}+b x+c=0$ , where $a≠0$ are given by the formula: To use the Quadratic Formula, we substitute the values of $a,b$ , and $c$ from the standard form into the expression on the right side of the formula. The solutions to a quadratic equation of the form $a x^{2}+b x+c=0, a \neq 0$ are given by the formula:
2.7.3: Solving Quadratic Equations
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_II_(2212)/02%3A_Math_Review/2.07%3A_Solving_Linear_Equations_and_Inequalities/2.7.03%3A_Solving_Quadratic_Equations
The solutions to a quadratic equation of the form $a x^{2}+b x+c=0$ , where $a≠0$ are given by the formula: To use the Quadratic Formula, we substitute the values of $a,b$ , and $c$ from the sta...The solutions to a quadratic equation of the form $a x^{2}+b x+c=0$ , where $a≠0$ are given by the formula: To use the Quadratic Formula, we substitute the values of $a,b$ , and $c$ from the standard form into the expression on the right side of the formula. The solutions to a quadratic equation of the form $a x^{2}+b x+c=0, a \neq 0$ are given by the formula:
2.8.4: Properties_of_Logarithms
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Introductory_Physics_II_(1112)/02%3A_Math_Review/2.08%3A_Functions/2.8.04%3A_Properties_of_Logarithms
\(\begin{array} {l c} {\text{Suppose we want to evaluate} \log_{a}M} & {\log_{a}M} \\ {\text{Let} \:y =\log_{a}M. }&{y=\log_{a}M} \\ {\text{Rewrite the epression in exponential form. }}&{a^{y}=M } \\ ... $\begin{array} {l c} {\text{Suppose we want to evaluate} \log_{a}M} & {\log_{a}M} \\ {\text{Let} \:y =\log_{a}M. }&{y=\log_{a}M} \\ {\text{Rewrite the epression in exponential form. }}&{a^{y}=M } \\ {\text{Take the }\:\log_{b} \text{of each side.}}&{\log_{b}a^{y}=\log_{b}M}\\ {\text{Use the Power Property.}}&{y\log_{b}a=\log_{b}M} \\ {\text{Solve for}\:y. }&{y=\frac{\log_{b}M}{\log_{b}a}} \\ {\text{Substiture}\:y=\log_{a}M.}&{\log_{a}M=\frac{\log_{b}M}{\log_{b}a}} \end{array}$
2.7.1: Solving Linera Equations
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_II_(2212)/02%3A_Math_Review/2.07%3A_Solving_Linear_Equations_and_Inequalities/2.7.01%3A_Solving_Linera_Equations
For an object moving at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula: For an object moving at a uniform (constant) rate, the distance tra...For an object moving at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula: For an object moving at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula: d=rt where d = distance, r = rate, t = time. To solve a formula for a specific variable means to get that variable by itself with a coefficient of 1 on one side of the equation and all other variables and constants on the other side.
2.7.2: Solving Inequalities
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_II_(2212)/02%3A_Math_Review/2.07%3A_Solving_Linear_Equations_and_Inequalities/2.7.02%3A_Solving_Inequalities
\[\begin{array} { l l } { \textbf { Subtraction Property of Inequality } } & { \textbf { Addition Property of Inequality } } \\ { \text { For any numbers } a , b , \text { and } c , } & { \text { For ...\[\begin{array} { l l } { \textbf { Subtraction Property of Inequality } } & { \textbf { Addition Property of Inequality } } \\ { \text { For any numbers } a , b , \text { and } c , } & { \text { For any numbers } a , b , \text { and } c } \\ { \text { if }\qquad \quad a < b } & { \text { if } \qquad \quad a < b } \\ { \text { then } a - c < b - c . } & { \text { then } a + c < b + c } \\\\ { \text { if } \qquad \quad a > b } & { \text { if } \qquad \quad a > b } \\ { \text { then } a - c > b -…
2.8.4: Properties_of_Logarithms
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_II_(2212)/02%3A_Math_Review/2.08%3A_Functions/2.8.04%3A_Properties_of_Logarithms
\(\begin{array} {l c} {\text{Suppose we want to evaluate} \log_{a}M} & {\log_{a}M} \\ {\text{Let} \:y =\log_{a}M. }&{y=\log_{a}M} \\ {\text{Rewrite the epression in exponential form. }}&{a^{y}=M } \\ ... $\begin{array} {l c} {\text{Suppose we want to evaluate} \log_{a}M} & {\log_{a}M} \\ {\text{Let} \:y =\log_{a}M. }&{y=\log_{a}M} \\ {\text{Rewrite the epression in exponential form. }}&{a^{y}=M } \\ {\text{Take the }\:\log_{b} \text{of each side.}}&{\log_{b}a^{y}=\log_{b}M}\\ {\text{Use the Power Property.}}&{y\log_{b}a=\log_{b}M} \\ {\text{Solve for}\:y. }&{y=\frac{\log_{b}M}{\log_{b}a}} \\ {\text{Substiture}\:y=\log_{a}M.}&{\log_{a}M=\frac{\log_{b}M}{\log_{b}a}} \end{array}$
2.7.1: Solving Linera Equations
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Introductory_Physics_II_(1112)/02%3A_Math_Review/2.07%3A_Solving_Linear_Equations_and_Inequalities/2.7.01%3A_Solving_Linera_Equations
For an object moving at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula: For an object moving at a uniform (constant) rate, the distance tra...For an object moving at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula: For an object moving at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula: d=rt where d = distance, r = rate, t = time. To solve a formula for a specific variable means to get that variable by itself with a coefficient of 1 on one side of the equation and all other variables and constants on the other side.

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