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2 years ago

10x - 8 > 2 (4x + 2) what is x

Mathematics

1 answer:

DIA [1.3K]2 years ago

3 0

Answer:

x>6

Step-by-step explanation:

10x-8 > 2(4x+2)

Distribute:

10x-8 > 8x+4

Add 8 to both sides/ Move the -8 to the right side by adding it

10x > 8x + 12

Subtract 8x from both sides

2x > 12

Simplify by dividing both sides by 2

x > 6

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If 2(4x + 3)/(x - 3)(x + 7) = a/x - 3 + b/x + 7, find the values of a and b.

zmey [24]

Answer:

$a=3$ and $b=5$ .

Step-by-step explanation:

So I believe the problem is this:

$\frac{2(4x+3)}{x-3}(x+7)}=\frac{a}{x-3}+\frac{b}{x+7}$

where we are asked to find values for $a$ and $b$ such that the equation holds for any $x$ in the equation's domain.

So I'm actually going to get rid of any domain restrictions by multiplying both sides by (x-3)(x+7).

In other words this will clear the fractions.

$\frac{2(4x+3)}{x-3}(x+7)}\cdot(x-3)(x+7)=\frac{a}{x-3}\cdot(x-3)(x+7)+\frac{b}{x+7}(x-3)(x+7)$

$2(4x+3)=a(x+7)+b(x-3)$

As you can see there was some cancellation.

I'm going to plug in -7 for x because x+7 becomes 0 then.

$2(4\cdot -7+3)=a(-7+7)+b(-7-3)$

$2(-28+3)=a(0)+b(-10)$

$2(-25)=0-10b$

$-50=-10b$

Divide both sides by -10:

$\frac{-50}{-10}=b$

$5=b$

Now we have:

$2(4x+3)=a(x+7)+b(x-3)$ with $b=5$

I notice that x-3 is 0 when x=3. So I'm going to replace x with 3.

$2(4\cdot 3+3)=a(3+7)+b(3-3)$

$2(12+3)=a(10)+b(0)$

$2(15)=10a+0$

$30=10a$

Divide both sides by 10:

$\frac{30}{10}=a$

$3=a$

So $a=3$ and $b=5$ .

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3 years ago

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Please help I’ll give brainliest

lesantik [10]

Answer: $108199

Step-by-step explanation:

Step 1) Find the deposit cost

35/100 × 89540 = 31339

Step 2) Find the total cost of the monthly payments

2135 × 36 = 76860

Step 3) Find the final cost

31339 + 76860 = $108199

4 0

3 years ago

2-13^3-10(23+21) = X

Tanya [424]

Answer:

x= -2635

Step-by-step explanation:

2 - 2197 - 10 x 44 = x

2- 2197 - 440 = x

-2635 = x

8 0

3 years ago

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What is the slope of (1,-5) and (3,-17)

Nikitich [7]

m(slope)= change in y/change in x

m=-17-(-5)/3-1

m=17+5/2

m=22/2

m=11

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3 years ago

It costs $74 per hour plus a $65 service fee to have a home theater system set up for you. Let t represent the number of hours.

ki77a [65]

Answer:

74t + 65= total cost

Step-by-step explanation:

74 is the amount per hour, so you would need to multiply that by the number of hours they work (74t) and the 65 is a set fee (does not change based on the amount of service) so you just add that on

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2 years ago