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2 years ago

Solve for X 3(x + 7) < 7(x + 2)

Mathematics

2 answers:

antiseptic1488 [7]2 years ago

7 0

$\\ \tt\hookrightarrow 3(x+7)$

$\\ \tt\hookrightarrow 3x+21$

$\\ \tt\hookrightarrow 3x-7x$

$\\ \tt\hookrightarrow -4x$

$\\ \tt\hookrightarrow 4x>7$

$\\ \tt\hookrightarrow x>7/4$

$\\ \tt\hookrightarrow x\in(\dfrac{7}{4},\infty)$

Furkat [3]2 years ago

5 0

Answer:

x > 7/4

Step-by-step explanation:

3(x + 7) < 7(x + 2)

Expand brackets: 3x + 21 < 7x + 14

Subtract 14 from both sides: 3x +7 < 7x

Subtract 3x from both sides: 7 < 4x

Divide both sides by 4: 7/4 < x

Therefore x > 7/4

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Sarah, Natasha and Richard share some sweets in the ratio 4:2:3. Sarah gets 13 more sweets than Richard. How many sweets are the

gayaneshka [121]

Answer:

117 sweets

Step-by-step explanation:

Please see attached picture for full solution. (model method)

S, N and R represents the number of sweets Sarah, Natasha and Richard have respectively.

Alternatively,

Let the number of sweets Sarah have be 4x.

Number of sweets Natasha have= 2x

Number of sweets Richard have= 3x

Sarah gets 13 more sweets than Richard

4x= 3x +13

4x -3x= 13

x= 13

Total number of sweets

= 4x +2x +3x

= 9x (simplify)

= 9(13) (subst. x=13)

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What two numbers can add to 4 but multiple to -12

olasank [31]

Answer:

Numbers: 6 and -2

Step-by-step explanation:

Equations

This question can be solved by inspection. It's just a matter of factoring 12 into two factors that sum 4. Both numbers must be of different signs and they are 6 and -2. Their sum is indeed 6-2=4 and their product is 6*(-2)=-12.

However, we'll solve it by the use of equations. Let's call x and y to the numbers. They must comply:

$x+y=4\qquad\qquad [1]$

$x.y=-12\qquad\qquad [2]$

Solving [1] for y:

$y=4-x$

Substituting in [2]

$x(4-x)=-12$

Operating:

$4x-x^2=-12$

Rearranging:

$x^2-4x-12=0$

Solving with the quadratic formula:

$\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

With a=1, b=-4, c=-12:

$\displaystyle x=\frac{-(-4)\pm \sqrt{(-4)^2-4(1)(-12)}}{2(1)}$

$\displaystyle x=\frac{4\pm \sqrt{16+48}}{2}$

$\displaystyle x=\frac{4\pm 8}{2}$

The solutions are:

$\displaystyle x=\frac{4+ 8}{2}=6$

$\displaystyle x=\frac{4- 8}{2}=-2$

This confirms the preliminary results.

Numbers: 6 and -2

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