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3 years ago

Solve for x.2 1/4x = 8 1/2

Mathematics

1 answer:

lorasvet [3.4K]3 years ago

6 0

Answer:

$\large\boxed{x=3\dfrac{7}{9}}$

Step-by-step explanation:

$2\dfrac{1}{4}x=8\dfrac{1}{2}\qquad\text{convert the mixed numbers to the improper fractions}\\\\\dfrac{2\cdot4+1}{4}x=\dfrac{8\cdot2+1}{2}\\\\\dfrac{9}{4}x=\dfrac{17}{2}\qquad\text{multiply both sides by 4}\\\\4\!\!\!\!\diagup^1\cdot\dfrac{9}{4\!\!\!\!\diagup_1}x=4\!\!\!\!\diagup^2\cdot\dfrac{17}{2\!\!\!\!\diagup_1}\\\\9x=(2)(17)\\\\9x=34\qquad\text{divide both sides by 9}\\\\x=\dfrac{34}{9}\\\\x=3\dfrac{7}{9}$

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So today i am learning how to subtract Intergers so i want to learn early so can you please tell me what -15 - ( - 8 ) = it woul

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1st you have to know that in mathematiques the signs preceding any number are of paramount importance:
1) addition of 2 digits with different signs:
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c) addition of 2 digits with both negative sign
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2) Multiplication: 2 digits with different signs:
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3) Multiplication: 2 digits with SAME signs;
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4) what applies on multiplication applies also on division (same principle)

5) Now we come to parenthesis: When you have parenthesis, the sign preceding the parenthesis is also of paramount importance:

a) a positive sign preceding a parenthesis doesn't affect the consents if you remove these parenthesis: +(5 + 3y) = 5+3y or 2(5+3y) = 10+6y

b) a NEGATIVE sign preceding a parenthesis DOES affect the consents if you remove these parenthesis:

-2(4x -2y -3) ==> If you remove the parenthesis by multiplying by (-2), all signs inside will change: the (+) become ( -) and vice versa,. However mind you, if you have a negative
Now let's take your equation: -15 - ( - 8 ) = -15 +8, remember a negative sign preceding any parenthesis will change all signs inside if you REMOVE the parenthesis: some examples:
a) -15 + 10 -(4-32x -4y)
1st (-15 + 10) = -5 since the largest number is preceded by a NEGATIVE sign
so : -5 - (4-32x -4y) remove the parenthesis -5 -4 + 32x +4y
b) -(-5-8) -(+5+8) ==> -5-8 -5-8 = -10 - 16 => - 26

.

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