Spell checked

StephenElston · StephenElston · commit 584ec48afafa · 2018-07-08T19:53:12.000-07:00
diff --git a/Module01/01-01-Introduction to Equations.ipynb b/Module01/01-01-Introduction to Equations.ipynb
@@ -133,7 +133,7 @@
     "\n",
     "\\begin{equation}\\textbf{5x} + 1 \\textbf{- 2x} = 22 \\end{equation}\n",
     "\n",
-    "In this equation, the left side includes the terms **5x** and **- 2x**, both of which represent the variable **x** multiplied by a coefficent. Note that we include the sign (+ or -) in front of the value.\n",
+    "In this equation, the left side includes the terms **5x** and **- 2x**, both of which represent the variable **x** multiplied by a coefficient. Note that we include the sign (+ or -) in front of the value.\n",
     "\n",
     "We can rewrite the equation to combine these like terms:\n",
     "\n",
@@ -151,7 +151,7 @@
     "\n",
     "\\begin{equation}3x = 21 \\end{equation}\n",
     "\n",
-    "Then we'll deal with the coefficients - in this case x is multiplied by 3, so we'll divide by 3 on boths sides to remove that:\n",
+    "Then we'll deal with the coefficients - in this case x is multiplied by 3, so we'll divide by 3 on both sides to remove that:\n",
     "\n",
     "\\begin{equation}\\frac{3x}{3} = \\frac{21}{3} \\end{equation}\n",
     "\n",
@@ -202,7 +202,7 @@
     "\n",
     "\\begin{equation}\\frac{x}{3} = 15 \\end{equation}\n",
     "\n",
-    "Now we need to deal with the fraction on the left so that we're left with just **x**. The fraction is <sup>x</sup>/<sub>3</sub> which is another way of saying *x divided by 3*, so we can apply the opposite operation to both sides. In this case, we need to multiply both sides by the denominator under our variable, which is 3. To make it easier to work with a term that contains fractions, we can express whole numbers as fractions with a denominator of 1; so on the left, we can express 3 as <sup>3</sup>/<sub>1</sub> and multiply it with <sup>x</sup>/<sub>3</sub>. Note that the notation for mutiplication is a **&bull;** symbol rather than the standard *x* multiplication operator (which would cause confusion with the variable **x**) or the asterisk symbol used by most programming languages.\n",
+    "Now we need to deal with the fraction on the left so that we're left with just **x**. The fraction is <sup>x</sup>/<sub>3</sub> which is another way of saying *x divided by 3*, so we can apply the opposite operation to both sides. In this case, we need to multiply both sides by the denominator under our variable, which is 3. To make it easier to work with a term that contains fractions, we can express whole numbers as fractions with a denominator of 1; so on the left, we can express 3 as <sup>3</sup>/<sub>1</sub> and multiply it with <sup>x</sup>/<sub>3</sub>. Note that the notation for multiplication is a **&bull;** symbol rather than the standard *x* multiplication operator (which would cause confusion with the variable **x**) or the asterisk symbol used by most programming languages.\n",
     "\n",
     "\\begin{equation}\\frac{3}{1} \\cdot \\frac{x}{3} = 15 \\cdot 3 \\end{equation}\n",
     "\n",
@@ -371,7 +371,7 @@
     "\n",
     "\\begin{equation}\\textbf{4(x + 2)} + \\textbf{3(x - 2)} = 16 \\end{equation}\n",
     "\n",
-    "The equation includes two operations in parenthesis: **4(*x* + 2)** and **3(*x* - 2)**. Each of these operations consists of a constant by which the contents of the parenthesis must be multipled: for example, 4 times (*x* + 2). The distributive property means that we can achieve the same result by multiplying each term in the parenthesis and adding the results, so for the first parenthetical operation, we can multiply 4 by *x* and add it to 4 times +2; and for the second parenthetical operation, we can calculate 3 times *x* + 3 times -2). Note that the constants in the parenthesis include the sign (+ or -) that preceed them:\n",
+    "The equation includes two operations in parenthesis: **4(*x* + 2)** and **3(*x* - 2)**. Each of these operations consists of a constant by which the contents of the parenthesis must be multiplied: for example, 4 times (*x* + 2). The distributive property means that we can achieve the same result by multiplying each term in the parenthesis and adding the results, so for the first parenthetical operation, we can multiply 4 by *x* and add it to 4 times +2; and for the second parenthetical operation, we can calculate 3 times *x* + 3 times -2). Note that the constants in the parenthesis include the sign (+ or -) that proceed them:\n",
     "\n",
     "\\begin{equation}4x + 8 + 3x - 6 = 16 \\end{equation}\n",
     "\n",
@@ -387,7 +387,7 @@
     "\n",
     "\\begin{equation}\\frac{7x}{7} = \\frac{14}{7} \\end{equation}\n",
     "\n",
-    "Which gives us our anwer:\n",
+    "Which gives us our answer:\n",
     "\n",
     "\\begin{equation}x = 2 \\end{equation}\n",
     "\n",
@@ -422,13 +422,6 @@
     "x = 2\n",
     "4*(x + 2) + 3*(x - 2) == 16"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {
