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2.2: Subtracting Integers
https://math.libretexts.org/Courses/Highline_College/Math_081_091%3A_CAM_Aligned_Textbook/02%3A_Arithmetic/2.02%3A_Subtracting_Integers
In Section 1.2, we stated that “Subtraction is the opposite of addition.” Thus, to subtract 4 from 7, we walked seven units to the right on the number line, but then walked 4 units in the opposite dir...In Section 1.2, we stated that “Subtraction is the opposite of addition.” Thus, to subtract 4 from 7, we walked seven units to the right on the number line, but then walked 4 units in the opposite direction (to the left), as shown in Figure $\PageIndex{1}$ . The key phrase is “add the opposite.” Thus, the subtraction 7 − 4 becomes the addition 7 + (−4), which we would picture on the number line as shown in Figure $\PageIndex{2}$ .
7.2: Rates and Slope
https://math.libretexts.org/Courses/Honolulu_Community_College/Math_75X%3A_Introduction_to_Mathematical_Reasoning_(Kearns)/07%3A_Introduction_to_Graphing/7.02%3A_Rates_and_Slope
Also, note that the magnitude (absolute value) of the slope of the second line is greater than the magnitude of the slope of the ﬁrst line. If $y$ is the dependent variable and $x$ is the independ...Also, note that the magnitude (absolute value) of the slope of the second line is greater than the magnitude of the slope of the ﬁrst line. If $y$ is the dependent variable and $x$ is the independent variable, then the slope is $\text {Slope}=\dfrac{\Delta y}{\Delta x} \nonumber$ where $\Delta y$ is the change in $y$ (diﬀerence in $y$ ) and $\Delta x$ is the change in $x$ (diﬀerence in $x$ ).
4.E: Systems of Linear Equations (Exercises)
https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_(Arnold)/04%3A_Systems_of_Linear_Equations/4.0E%3A_4.E%3A_Systems_of_Linear_Equations_(Exercises)
3) $\begin{aligned} 2 x+y &=6 \\ y &=x+3 \end{aligned}$ In Exercises 7-18, solve each of the given systems by sketching the lines represented by each equation of the given system on graph paper, the...3) $\begin{aligned} 2 x+y &=6 \\ y &=x+3 \end{aligned}$ In Exercises 7-18, solve each of the given systems by sketching the lines represented by each equation of the given system on graph paper, then estimating the coordinates of the point of intersection to the nearest tenth. 12) $\begin{aligned} 4 x+3 y &=24 \\ y &=\dfrac{1}{7} x+5 \end{aligned}$ 20) $\begin{aligned} 3 x+6 y &=2 \\ y &=-2 y+2 \end{aligned}$ 28) $\begin{aligned} 9 x+4 y &=-3 \\ y &=-\dfrac{9}{4} x+6 \end{aligned}$
1.8: What to Combine? Order of Operations with Integers
https://math.libretexts.org/Courses/Honolulu_Community_College/Math_75X%3A_Introduction_to_Mathematical_Reasoning_(Kearns)/01%3A_Whole_Numbers_and_Integers/1.08%3A_What_to_Combine__Order_of_Operations_with_Integers
\[ \begin{aligned} \frac{-5-5(2-4)^3}{-22-3(-5)} = \frac{-5-5(-2)^3}{-22-(-15)} ~ & \begin{array}{l} \textcolor{red}{ \text{ Numerator: parentheses first.}} \\ \textcolor{red}{ \text{ Denominator: mul...\[ \begin{aligned} \frac{-5-5(2-4)^3}{-22-3(-5)} = \frac{-5-5(-2)^3}{-22-(-15)} ~ & $\begin{array}{l} \textcolor{red}{ \text{ Numerator: parentheses first.}} \\ \textcolor{red}{ \text{ Denominator: multiply } 3(-5)=-15.} \end{array}$ \\ = \frac{-5-5(-8)}{-22+15} ~ & $\begin{array}{l} \textcolor{red}{ \text{ Numerator: exponent } (-2)^3 = -8.} \\ \textcolor{red}{ \text{ Denominator: add the opposite.}} \end{array}$ \\ = \frac{-5-(-40)}{-7} & \begin{array}{l} \textcolor{red}{ \text{ Numerator: multip…
6.3: Applications of Polynomials
https://math.libretexts.org/Courses/Hawaii_Community_College/Hawaii_Community_College_MA82X_Textbook/06%3A_Polynomial_Functions/6.03%3A_Applications_of_Polynomials
Use the arrow keys to move the cursor slightly to the left of the $t$ -intercept, then press ENTER in response to “Left bound.” Move your cursor slightly to the right of the t-intercept, then press E...Use the arrow keys to move the cursor slightly to the left of the $t$ -intercept, then press ENTER in response to “Left bound.” Move your cursor slightly to the right of the t-intercept, then press ENTER in response to “Right bound.” Leave your cursor where it is and press ENTER in response to “Guess.” The result is shown in Figure $\PageIndex{11}$ .
4.9: Interest
https://math.libretexts.org/Courses/Barton_Community_College/Book%3A_Technical_Mathematics_(Turner)/04%3A_Business_Math/4.09%3A_Interest
where I is the interest, P is the principal, r is the interest rate, and t is the time. The principal is P = $5000, the interest rate is r = 4.5% = 0.045 per year, and the time or duration of the loan...where I is the interest, P is the principal, r is the interest rate, and t is the time. The principal is P = $5000, the interest rate is r = 4.5% = 0.045 per year, and the time or duration of the loan is t = 6 months. The interest owed is I = $90, the interest rate is r = 5.4% = 0.054 per year, and the time or duration of the loan is t = 4 months. where A is the balance, P is the principal, r is the simple interest rate, and t is the duration of the loan or investment.
5.4: Adding and Subtracting Polynomials
https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_(Arnold)/05%3A_Polynomial_Functions/5.04%3A_Adding_and_Subtracting_Polynomials
In this section we concentrate on adding and subtracting polynomial expressions, based on earlier work combining like terms in Ascending and Descending Powers.
2.2.4: Simplifying Algebraic Expressions
https://math.libretexts.org/Courses/Nova_Scotia_Community_College/MATH_1043/02%3A_Algebra/2.02%3A_The_Fundamentals_of_Algebra/2.2.04%3A_Simplifying_Algebraic_Expressions
The commutative property allows us to change the order of multiplication without affecting the product or answer. The associative property allows us to regroup without affecting the product or answer.
6: Polynomial Functions
https://math.libretexts.org/Courses/Hawaii_Community_College/Hawaii_Community_College_MA82X_Textbook/06%3A_Polynomial_Functions
6.E: Polynomial Functions (Exercises)
https://math.libretexts.org/Courses/Hawaii_Community_College/Hawaii_Community_College_MA82X_Textbook/06%3A_Polynomial_Functions/6.E%3A_Polynomial_Functions_(Exercises)
Find the volume of the box as a function of $x$ , the measure of the side of each square cut from the four corner of the original piece of cardboard. Find the surface area of the box as a function of...Find the volume of the box as a function of $x$ , the measure of the side of each square cut from the four corner of the original piece of cardboard. Find the surface area of the box as a function of $x$ , the measure of the side of each square cut from the four corner of the original piece of cardboard.
6.4: Adding and Subtracting Polynomials
https://math.libretexts.org/Courses/Hawaii_Community_College/Hawaii_Community_College_MA82X_Textbook/06%3A_Polynomial_Functions/6.04%3A_Adding_and_Subtracting_Polynomials
In this section we concentrate on adding and subtracting polynomial expressions, based on earlier work combining like terms in Ascending and Descending Powers.

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