Here's your expression with corrected grammar and without unnecessary words: [tex]8 = -18 + \frac{3}{8}(16 - 40n)[/tex] Please note that the expression itself doesn't have grammatical issues since mathematical expressions follow their own syntax rules, which are different from linguistic grammar. But if you want the equation to be more concise, the version I provided is already stripped of any extraneous wording.

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Here's your expression with corrected grammar and without unnecessary words: [tex]8 = -18 + \frac{3}{8}(16 - 40n)[/tex] Please note that the expression itself doesn't have grammatical issues since mathematical expressions follow their own syntax rules, which are different from linguistic grammar. But if you want the equation to be more concise, the version I provided is already stripped of any extraneous wording.

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Categories: MathematicsCollege

createdby: Anonymous

Status: Active

Is Flagged: No

Created At: Feb 4, 2021, 6:21:23 PM

Answer: To solve the expression `[tex]8 = -18 + \frac{3}{8}(16 - 40n)[/tex]`, we follow these steps:

Step 1: Distribute the `[tex]\frac{3}{8}[/tex]` to both terms inside the parentheses. This means we multiply `[tex]\frac{3}{8}[/tex]` by 16 and `[tex]\frac{3}{8}[/tex]` by `-40n`:

`[tex]8 = -18 + \frac{3}{8} \times 16 + \frac{3}{8} \times (-40n)[/tex]`

Step 2: Simplify the multiplicative terms.

`[tex]\frac{3}{8} \times 16 = 6[/tex]` because `[tex]\frac{3}{8} \times 16 = \frac{3 \times 16}{8} = \frac{48}{8} = 6[/tex]`

`[tex]\frac{3}{8} \times (-40n) = -15n[/tex]` because `[tex]\frac{3 \times (-40)n}{8} = \frac{-120n}{8} = -15n[/tex]`

Step 3: Substitute the simplified terms back into the equation.

`[tex]8 = -18 + 6 - 15n[/tex]`

Step 4: Combine the like terms on the right side of the equation.

`[tex]8 = -12 - 15n[/tex]` because `-18 + 6 = -12`

Step 5: Add 12 to both sides to isolate terms with `n` on one side.

`[tex]8 + 12 = -12 + 12 - 15n[/tex]`

Thus,

`[tex]20 = -15n[/tex]`

Step 6: Finally, divide by `-15` to solve for `n`.

`[tex]n = \frac{20}{-15}[/tex]` which simplifies to `[tex]n = -\frac{4}{3}[/tex]` or `[tex]n = -1\frac{1}{3}[/tex]`

Your equation solved for `n` is:

`[tex]n = -\frac{4}{3}[/tex]`

Extra: Solving algebraic equations with fractions can be intimidating, but if you follow systematic steps, you can simplify the process. Before you start, it's essential to understand the properties of equality (what you do to one side of the equation, you must do to the other) and the distributive property, which allows you to multiply a term outside the parentheses to each term inside the parentheses.

Additionally, combining like terms helps simplify the equation by grouping numbers and variables separately, which makes it easier to isolate the variable you are solving for.

Understanding fractions and operations with fractions is also crucial since they often appear in algebraic expressions. When you multiply or divide both sides of an equation by fractions, you are applying the same principles as you would with whole numbers, keeping the equation balanced.

Lastly, it's important for students to remember that dividing by a negative number will change the sign of the result. This is exactly what happened in the final step when dividing both sides by `-15` to solve for `n`.