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To beginning algebra students, literal equations, those involving more than one letter, often seem inherently more difficult to solve than simpler, univariate on es.  But this isn’t so.  The trick is to treat the extra letters like simple numerals using the same steps you would ordinarily. Solving equations is a matter of “undoing” what’s been done to the variable, using inverse operations, starting as far from the variable as possible. - Example 1 To solve 3(x+4)–8 = 19, we first undo subtracting 8 by adding 8, then divide by 3 to undo multiplying by 3, and finally subtract 4 to undo adding 4. The result is x = 5. [Note: we could first simplify by distributing 3 across (x+4) and adding like terms, but this would take four steps, not three.] If the letters a, b, and c were to replace 3, 4, and 19 in the same equation, we’d carry out exactly the same series of steps. This time we’d start with a(x+b)–8 = c. We’d then add 8, divide by a, then subtract b to get x = (c+8)/a – b. W...

To beginning algebra students, literal equations, those involving more than one letter, often seem inherently more difficult to solve than simpler, univariate on es.  But this isn’t so.  The trick is to treat the extra letters like simple numerals using the same steps you would ordinarily. Solving equations is a matter of “undoing” what’s been done to the variable, using inverse operations, starting as far from the variable as possible. - Example 1 To solve 3(x+4)–8 = 19, we first undo subtracting 8 by adding 8, then divide by 3 to undo multiplying by 3, and finally subtract 4 to undo adding 4. The result is x = 5. [Note: we could first simplify by distributing 3 across (x+4) and adding like terms, but this would take four steps, not three.] If the letters a, b, and c were to replace 3, 4, and 19 in the same equation, we’d carry out exactly the same series of steps. This time we’d start with a(x+b)–8 = c. We’d then add 8, divide by a, then subtract b to get x = (c+8)/a – b. W...

To beginning algebra students, literal equations, those involving more than one letter, often seem inherently more difficult to solve than simpler, univariate on es.  But this isn’t so.  The trick is to treat the extra letters like simple numerals using the same steps you would ordinarily. Solving equations is a matter of “undoing” what’s been done to the variable, using inverse operations, starting as far from the variable as possible. - Example 1 To solve 3(x+4)–8 = 19, we first undo subtracting 8 by adding 8, then divide by 3 to undo multiplying by 3, and finally subtract 4 to undo adding 4. The result is x = 5. [Note: we could first simplify by distributing 3 across (x+4) and adding like terms, but this would take four steps, not three.] If the letters a, b, and c were to replace 3, 4, and 19 in the same equation, we’d carry out exactly the same series of steps. This time we’d start with a(x+b)–8 = c. We’d then add 8, divide by a, then subtract b to get x = (c+8)/a – b. W...

The online Desmos graphing calculator is fast taking over from the venerable Ti-84 series  of handheld calculators as the default calculator tool in secondary education. Desmos is now included as an integral part of the digital SAT, and acquiring intermediate-level Desmos skills is fundamental to maximizing math scores. [Familiarity with the Ti-84 Plus CE handheld graphing calculator is still crucial to optimizing math scores on the ACT.] I'm not aware of any succinct, comprehensive exposition of Desmos skills required for use on the dSAT (I'm working on it). At this point, the best one can do is to peruse the various official materials linked in the "Desmos First Steps" and "Desmos Graphing Calculator" sections below.  Check out each link, read the information provided, and do the sample exercises until you've covered all topics presented (search Google for additional help with particular topics). - Desmos First Steps User Guide Quick Start Guide Gett...

The online Desmos graphing calculator is fast taking over from the venerable Ti-84 series  of handheld calculators as the default calculator tool in secondary education. Desmos is now included as an integral part of the digital SAT, and acquiring intermediate-level Desmos skills is fundamental to maximizing math scores. [Familiarity with the Ti-84 Plus CE handheld graphing calculator is still crucial to optimizing math scores on the ACT.] I'm not aware of any succinct, comprehensive exposition of Desmos skills required for use on the dSAT (I'm working on it). At this point, the best one can do is to peruse the various official materials linked in the "Desmos First Steps" and "Desmos Graphing Calculator" sections below.  Check out each link, read the information provided, and do the sample exercises until you've covered all topics presented (search Google for additional help with particular topics). - Desmos First Steps User Guide Quick Start Guide Gett...

The online Desmos graphing calculator is fast taking over from the venerable Ti-84 series  of handheld calculators as the default calculator tool in secondary education. Desmos is now included as an integral part of the digital SAT, and acquiring intermediate-level Desmos skills is fundamental to maximizing math scores. [Familiarity with the Ti-84 Plus CE handheld graphing calculator is still crucial to optimizing math scores on the ACT.] I'm not aware of any succinct, comprehensive exposition of Desmos skills required for use on the dSAT (I'm working on it). At this point, the best one can do is to peruse the various official materials linked in the "Desmos First Steps" and "Desmos Graphing Calculator" sections below.  Check out each link, read the information provided, and do the sample exercises until you've covered all topics presented (search Google for additional help with particular topics). - Desmos First Steps User Guide Quick Start Guide Gett...