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Math Help - linear equations

  1. #1
    Spoonman
    Guest

    Exclamation linear equations

    I need some help with the following problems. If you could, please show me how to find the correct answers, since I know what the correct answers are already. I'm taking my Midterm on Tuesday. So, I would like to see some replies by tomorrow. I will also post some new problems tomorrow and maybe even on Monday. Thanks in advance for those who can help me.

    Linear Equations

    1.) <br />
\frac{1}{2}x -\frac{7}{4} = -\frac{3}{4}x + 5<br />

    Correct Answer:

    <br />
x = \frac{27}{5}<br />

    2.) <br />
\frac{2}{3}x -\frac{11}{6} = 1 -\frac{3}{4}x<br />

    Correct Answer:

    <br />
x = 2<br />

    Literal Equations

    1.) The surface area of a cylinder is given by the following equation. Solve it for h:

    <br />
S = 2(pi)rh + 2(pi)r^2<br />

    Correct Answer:

    <br />
h = \frac{S - 2(pi)r^2}{2(pi)r}<br />

    2.) <br />
|5x - 1| = -4<br />

    Correct Answer:

    No Solution

    3.) <br />
|3x - 2| \geq -2<br />

    Correct Answer:

    All Real Numbers

    4.) <br />
|5x - 2| < -4<br />

    Correct Answer:

    No Solution

    5.) Solve for y:

    <br />
x = \frac{2}{3}(y + 4)<br />

    Correct Answer:

    <br />
y = \frac{3}{2}x - 4<br />

    Inequalities

    1.) <br />
2x + 1 \leq 6x - 1<br />
OR <br />
4x - 7 \leq -11<br />

    Correct Answer:

    <br />
x \geq \frac{1}{2}<br />
OR <br />
x \leq -1<br />

    2.) <br />
-1 \leq -2x + 1 < 5<br />

    Correct Answer:

    No Solution

    Absolute Value Equations

    1.) <br />
|3x + 2| = 10<br />

    Correct Answer:

    <br />
x = \frac{8}{3}<br />
    <br />
x = -4<br />

    2.) <br />
2|5x - 1| + 12 = 4<br />

    Correct Answer:

    No Solution

    3.) <br />
2|3x - 4| + 4 = 8<br />

    Correct Answer:

    <br />
x = \frac{2}{3}<br />
    <br />
x = 2<br />

    4.) <br />
|\frac{1}{2}x - 3| + 5 = 11<br />

    Correct Answer:

    <br />
x = -6<br />
    <br />
x = 18<br />

    5.) <br />
|3x + 2| < 8<br />

    Correct Answer:

    <br />
x < 2<br />
AND <br />
x > \frac{-10}{3}<br />

    6.) <br />
2|x - 3| + 5 \geq 17<br />

    Correct Answer:

    <br />
x \geq 9<br />
OR <br />
x \leq -3<br />

    7.) <br />
|5x - 7| < 5 -3<br />

    Correct Answer:

    No Solution

    7.) <br />
4|3x + 5| + 9 > 1<br />

    Correct Answer:

    All Real Numbers

    Order Of Operations

    1.) Simplify:

    <br />
-3^2 + [4(2^2 - 1) + 6]3 -(-2)<br />

    Correct Answer:

    <br />
47<br />

    2.) Evaluate x^3 + x^2 + x when x = -3:

    Correct Answer:

    <br />
-21<br />

    3.) Evaluate the following when a = 2, b = -3, and c = -4:

    <br />
\frac{a^3 + b^2 + c^2}{|abc|} =<br />

    Correct Answer:

    <br />
\frac{11}{8}<br />
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  2. #2
    Flow Master
    mr fantastic's Avatar
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    Thats' quite a mountain of work, sport! I'll give a few tips for the first few.
    Quote Originally Posted by Spoonman View Post
    [snip]
    Linear Equations

    1.) <br />
\frac{1}{2}x -\frac{7}{4} = -\frac{3}{4}x + 5<br />

    Mr F says: Multiply the whole of the equation through by 4 and solve the resulting much simpler linear equation. Note: 4 is the lowest common multiple of 2 and 4, the numbers in the denominators of the fractions.

    Correct Answer:

    <br />
x = \frac{27}{5}<br />

    2.) <br />
\frac{2}{3}x -\frac{11}{6} = 1 -\frac{3}{4}x<br />

    Mr F says: Multiply the whole of the equation through by 12 and solve the resulting much simpler linear equation. Note: 12 is the lowest common multiple of 3, 6 and 4, the numbers in the denominators of the fractions.

    Correct Answer:

    <br />
x = 2<br />

    Literal Equations

    1.) The surface area of a cylinder is given by the following equation. Solve it for h:

    <br />
S = 2(pi)rh + 2(pi)r^2<br />

    Mr F says: Step 1: Subtract 2 \pi r^2 from both sides. Step 2: Divide both sides by 2 \pi r.

    Correct Answer:

    <br />
h = \frac{S - 2(pi)r^2}{2(pi)r}<br />

    2.) <br />
|5x - 1| = -4<br />

    Mr F says: Can a magnitude ever be negative? Therefore .....

    Correct Answer:

    No Solution

    3.) <br />
|3x - 2| \geq -2<br />

    Mr F says: A magnitude is always gretare than or equal to 0. Therefore ......


    Correct Answer:

    All Real Numbers

    4.) <br />
|5x - 2| < -4<br />

    Mr F says: Can a magnitude ever be negative? Therefore .....

    Correct Answer:

    No Solution

    5.) Solve for y:

    <br />
x = \frac{2}{3}(y + 4)<br />

    Mr F says: Step 1: Multiply the whole equation through by 3. Step2: Expand the right hand side. Step 3: Subtract 8 from both sides. Step 4: Make y the subject. Note that \frac{3x - 8}{2} = \frac{3x}{2} - \frac{8}{2} = \frac{3}{2}x - 4.

    Correct Answer:

    <br />
y = \frac{3}{2}x - 4<br />

    Inequalities

    1.) <br />
2x + 1 \leq 6x - 1<br />
OR <br />
4x - 7 \leq -11<br />

    Correct Answer:

    <br />
x \geq \frac{1}{2}<br />
OR <br />
x \leq -1<br />

    2.) <br />
-1 \leq -2x + 1 < 5<br />

    Correct Answer:

    No Solution

    Absolute Value Equations

    1.) <br />
|3x + 2| = 10<br />

    Correct Answer:

    <br />
x = \frac{8}{3}<br />
    <br />
x = -4<br />

    2.) <br />
2|5x - 1| + 12 = 4<br />

    Mr F says: Step 1: Subtract 12 from both sides. Step 2: Divide both sides by 2. Step 3: Can a magnitude ever be negative? Therefore .....

    Correct Answer:

    No Solution

    3.) <br />
2|3x - 4| + 4 = 8<br />

    Correct Answer:

    <br />
x = \frac{2}{3}<br />
    <br />
x = 2<br />

    4.) <br />
|\frac{1}{2}x - 3| + 5 = 11<br />

    Correct Answer:

    <br />
x = -6<br />
    <br />
x = 18<br />

    5.) <br />
|3x + 2| < 8<br />

    Correct Answer:

    <br />
x < 2<br />
AND <br />
x > \frac{-10}{3}<br />

    6.) <br />
2|x - 3| + 5 \geq 17<br />

    Correct Answer:

    <br />
x \geq 9<br />
OR <br />
x \leq -3<br />

    7.) <br />
|5x - 7| < 5 -3<br />

    InCorrect Answer:

    No Solution

    7.) <br />
4|3x + 5| + 9 > 1<br />

    Mr F says: Step 1: Subtract 9 from both sides. Step 2: Divide both sides by 4. Step 3: A magnitude is always gretare than or equal to zero. Therefore .....

    Correct Answer:

    All Real Numbers

    Order Of Operations

    1.) Simplify:

    <br />
-3^2 + [4(2^2 - 1) + 6]3 -(-2)<br />

    Mr F says: [tex]= -9 + [4(4 - 1) + 6]3 + 2 = ....

    Correct Answer:

    <br />
47<br />

    2.) Evaluate x^3 + x^2 + x when x = -3:

    Mr F says: [tex]= (-3)^3 + (-3)^2 + (-3) = -27 + 9 - 3 = ....

    Correct Answer:

    <br />
-21<br />

    3.) Evaluate the following when a = 2, b = -3, and c = -4:

    <br />
\frac{a^3 + b^2 + c^2}{|abc|} =<br />

    Mr F says: Substitute the given values. Note that 2^3 = 8, (-3)^2 = 9, (-4)^2 = 16, |(2)(-3)(-4)| = |24| = 24 ......

    Correct Answer:

    <br />
\frac{11}{8}<br />
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  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
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    Wellsville, NY
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    Quote Originally Posted by Spoonman View Post
    I need some help with the following problems. If you could, please show me how to find the correct answers, since I know what the correct answers are already. I'm taking my Midterm on Tuesday. So, I would like to see some replies by tomorrow. I will also post some new problems tomorrow and maybe even on Monday. Thanks in advance for those who can help me.
    I don't think anyone minds helping you, but the amount of work here is ridiculous. Either post the ones that you can't do or show us what work you've done on them. It will help us post answers that are more useful to you and not use up nearly as much effort.

    -Dan
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