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Bond [772]
3 years ago
7

Which expressions are equivalent to 7 (negative three-fourths x minus 3)? Select two options.

Mathematics
2 answers:
polet [3.4K]3 years ago
7 0

<em><u>The equivalent expressions are:</u></em>

7(-\frac{3}{4}x - 3) = (7 \times \frac{-3}{4}x) + (7 \times -3)\\\\7(-\frac{3}{4}x - 3) = \frac{-21x}{4} - 21

<em><u>Solution:</u></em>

<em><u>Given expression is:</u></em>

7(-\frac{3}{4}x - 3)

We have to find the equivalent expressions

By distributive property,

a(b + c) = ab + ac

Therefore,

7(-\frac{3}{4}x - 3) = (7 \times \frac{-3}{4}x) + (7 \times -3)\\\\7(-\frac{3}{4}x - 3) = \frac{-21x}{4} - 21

Thus equivalent expressions are found

Elan Coil [88]3 years ago
7 0

Answer:

Im pretty sure its a and e

Step-by-step explanation:

lmk if im wrong or right

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GaryK [48]

Answer:

  • The two solutions are:           x=\frac{1}{2}+/-\frac{\sqrt{7} }{2}

  • The next and every step are below.

Explanation:

1. -3=-2x^2+2x    : Given (addition property / add - 3 to both sides)

2. -3 = - 2(x^2-x)    : Given (commom factor - 2)

3. -3-1/2=-2(x^2-x+1/4)

    To obtain the perfect square it was added the square of half of the coefficient of x: (1/2)² = 1/4, inside the parenthesis.

Since, the terms inside the parentthesis are multiplied by - 2, you have to add - 2 (1/4) = - 1/2 to the left side of the equation.

4. Now, you have that the trinomial x² - x + 1/4 is a square perfect trinomial which is factored as (x - 1/2)² and get the expression:

-7/2=-2(x-1/2)^2

5. Divide both sides by - 2 to get the next expression:

-7/4=(x-1/2)^2

6. The last step is to extract squere root from both sides of the equality:

(x-1/2)=+/-\sqrt{\frac{7}{4}}\\ \\ x-1/2=+/-\frac{\sqrt{7} }{2}\\ \\ x=\frac{1}{2}+/-\frac{\sqrt{7} }{2}

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