9th Grade
How Do You Create and Solve Inequalities in One Variable Using Addition and Subtraction?
{
"voice_prompt": "",
"manuscript": {
"title": {
"text": "How Do You Create and Solve Inequalities in One Variable Using Addition and Subtraction?",
"audio": "How do you create and solve inequalities in one variable using addition and subtraction?"
},
"description": {
"text": "To solve inequalities in one variable using addition or subtraction: 1. Understand the situation. 2. Write the inequality with the correct symbol. 3. Solve it by isolating the variable. 4. Check your answer to be sure it works.",
"audio": "To solve inequalities in one variable using addition or subtraction: 1. Understand the situation. 2. Write the inequality with the correct symbol. 3. Solve it by isolating the variable. 4. Check your answer to be sure it works."
},
"scenes": [
{
"text": "Inequalities help you describe situations where more than one value can work. You use the symbols less than, greater than, less than or equal to, and greater than or equal to to compare quantities and show a whole range of solutions.",
"latex": "<, >, \\leq, \\geq",
"pop_animation_prompt": "Create pop animations for the following math elements as they are referenced: First, pop the \"<\" symbol when \"less than\" is mentioned. Next, pop the \">\" symbol with \"greater than.\" Then, pop the \"\\leq\" symbol with \"less than or equal to.\" Finally, pop the \"\\geq\" symbol with \"greater than or equal to.\" Ensure each symbol pops at the exact moment it is referenced in the transcript for clarity and emphasis."
},
{
"text": "Let\u2019s start with a real-world example. You want to save at least fifty dollars to buy a game. You already have twenty dollars. How much more do you need to save?",
"latex": "x + 20 \\geq 50",
"pop_animation_prompt": "Create pop animations for the mathematical expression \"x + 20 \\\\geq 50\" as follows: First, pop the operator \"\\geq\" (index 6) when \"at\" is mentioned. Next, pop the number \"50\" (index 7) when \"fifty\" is mentioned. Finally, pop the number \"20\" (index 3) when \"twenty\" is mentioned. Ensure each element pops at the precise moment it is referenced in the transcript."
},
{
"text": "Let x represent the amount you still need to save. Since your total savings should be at least fifty dollars, you write the inequality: x plus twenty is greater than or equal to fifty.",
"latex": "x + 20 \\geq 50 + b",
"pop_animation_prompt": "Create pop animations for the following elements in sequence: First, pop \"x\" when mentioned as the amount to save. Next, pop \"50\" when referenced as the total savings. Then, pop \"x\", \"+\", and \"20\" together when the inequality is introduced. Finally, pop \"\\geq\" and \"50\" when the comparison is explained. Ensure each pop aligns with its respective reference in the transcript."
},
{
"text": "Next, solve the inequality by isolating x. Subtract twenty from both sides. This gives you x is greater than or equal to thirty. So you need to save thirty dollars or more.",
"latex": "x + 20 - 20 \\geq 50 - 20 \\quad x \\geq 30",
"pop_animation_prompt": "Create pop animations for the following elements in sequence: First, pop the symbol \"x\" (index 1) when mentioned. Next, pop the number \"20\" (index 3) when referenced. Then, pop the symbol \"x\" (index 1) again, followed by the operator \"\\(\\geq\\)\" (index 19) and the number \"30\" (index 20) simultaneously. Finally, pop the number \"30\" (index 20) once more when reiterated. Ensure each pop aligns with its respective mention in the transcript."
},
{
"text": "Check your answer. Plug in thirty for x. You get thirty plus twenty equals fifty, and fifty is greater than or equal to fifty \u2014 so the solution works.",
"latex": "30 + 20 = 50 \\quad 50 \\geq 50",
"pop_animation_prompt": "Create pop animations for the following sequence: First, pop \"30\" when referenced as \"thirty\" for x. Next, pop \"30\" and \"20\" together when mentioned as \"thirty plus twenty\". Then, pop \"50\" when referred to as \"equals fifty\". Finally, pop the \"\u2265\" symbol and \"50\" together when described as \"greater than or equal to fifty\". Ensure each pop aligns with its respective reference in the transcript."
},
{
"text": "Now here\u2019s a subtraction example. You had forty dollars, and you spent some of it. You want to make sure you still have at least ten dollars left. How much can you spend at most?",
"latex": "40 - x",
"pop_animation_prompt": "Create pop animations for the mathematical expression \"40 - x\". First, pop the subtraction operator \"-\" when the word \"subtraction\" is mentioned. Then, pop the number \"40\" when the word \"forty\" is mentioned. Ensure these elements pop in sequence as they are referenced in the transcript."
},
{
"text": "Let x be the amount you spend. Since you want to have at least ten dollars left, you write the inequality: forty minus x is greater than or equal to ten.",
"latex": "40 - x \\geq 10",
"pop_animation_prompt": "Create pop animations for the following elements in sequence as they are referenced: First, pop \"x\" when mentioned as the amount spent. Next, pop \"10\" when discussing the amount left. Then, pop \"40\", \"-\", and \"x\" together when forming the inequality. Finally, pop \"\\geq\" and \"10\" together to complete the inequality statement. Ensure each pop aligns with the corresponding reference in the transcript for clarity."
},
{
"text": "Now solve the inequality. Start by getting rid of the minus x on the left side. You do that by adding x to both sides.",
"latex": "40 - x + x \\geq 10 + x",
"pop_animation_prompt": "Create pop animations for the mathematical expression. First, pop the minus sign and the x on the left side: elements S8.- and S8.x. Then, pop the x terms on both sides: elements S8.x, S8.x.3, and S8.x.4. Ensure the pops occur in sequence as referenced in the transcript."
},
{
"text": "Now the left side becomes 40, and the right side is 10 plus x.",
"latex": "40 \\geq 10 + x",
"pop_animation_prompt": "Create pop animations for the mathematical expression \"40 \\geq 10 + x\". First, pop the number \"40\" when referenced. Next, pop the number \"10\" and the symbol \"x\" simultaneously when they are mentioned together. Ensure each element pops at the time it is referenced in the transcript."
},
{
"text": "Next, subtrackt 10 from both sides to get rid of the 10 next to x.",
"latex": "40 - 10 \\geq 10 + x - 10",
"pop_animation_prompt": "Create pop animations for the mathematical expression \"40 - 10 \\\\geq 10 + x - 10\". First, pop the number \"10\" at index 5. Then, simultaneously pop the number \"10\" at index 15. Ensure these elements pop when referenced in the transcript to highlight the subtraction of \"10\" from both sides of the inequality."
},
{
"text": "That gives you 30 is greater than or equal to x. That means x is less than or equal to thirty. You can spend up to thirty dollars.",
"latex": "30 \\geq x",
"pop_animation_prompt": "Create pop animations for the mathematical expression \"30 \\geq x\" as follows: First, pop the entire expression \"30 \\geq x\" when it is first mentioned. Then, pop the symbol \"x\" and the operator \"\\geq\" simultaneously when \"x is less than or equal to\" is stated. Finally, pop the number \"30\" when \"thirty\" is mentioned, and again when \"thirty dollars\" is referenced."
},
{
"text": "Check your answer. Try x equals thirty. Forty minus thirty equals ten \u2014 and that\u2019s exactly what you need left. So it works.",
"latex": "40 - 30 = 10",
"pop_animation_prompt": "Create pop animations for the mathematical expression \"40 - 30 = 10\" as follows: First, pop the number \"30\" when referenced. Next, pop \"40\", followed by the operator \"-\", then \"30\" again. After that, pop the \"=\" operator, and finally, pop the number \"10\". Ensure each element pops at the moment it is mentioned in the transcript to maintain pedagogical flow."
},
{
"text": "Inequalities help you show a full range of possible answers. Whether you're saving money or sticking to a limit, writing and solving an inequality helps you know what values will work.",
"latex": "x \\geq 30, \\quad x \\leq 30",
"pop_animation_prompt": "Create pop animations for the expression \"x \\geq 30, \\quad x \\leq 30\" when referenced. First, pop \"x \\geq 30\" as a group, highlighting \"x\", \"\\geq\", and \"30\". Then, pop \"x \\leq 30\" as a group, highlighting \"x\", \"\\leq\", and \"30\". Ensure both inequalities are visually distinct to emphasize the range of possible values."
}
],
"outro": {
"text": "To solve inequalities in one variable using addition or subtraction: 1. Understand the situation. 2. Write the inequality with the correct symbol. 3. Solve it by isolating the variable. 4. Check your answer to be sure it works.",
"audio": "To solve inequalities in one variable using addition or subtraction: 1. Understand the situation. 2. Write the inequality with the correct symbol. 3. Solve it by isolating the variable. 4. Check your answer to be sure it works."
}
}
}
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