For the equation 2(4x+10)=8x+k what value of k will create an equation with infinitely many solutions?
2 answers:
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Answer: x≤ -0.5
Step-by-step explanation: Graph the two lines or solve for x:
2x – 6 ≥ 6(x – 2) + 8
2x – 6 ≥ 6x – 12 + 8
2x – 6 ≥ 6x – 4
-4x ≥ 2
x ≤ -1/2 [Inequality is reversed when multiplying or dividing by a negative number]
The number line is anything less than or equal to - 1/2
Or one can plot each side of the inequality and note the interception point (x = -(1/2)).
1) Resultant fraction:
2) Total soil: pounds
3) Result of the product:
Step-by-step explanation:
1)
In this problem, we want to find the product between the two fractions
and
In order to find this product, we have to multiply the numerators of each fraction and the denominators of each fraction. We get:
Now we simplify, dividing both numerator and denominator by 2:
And the fraction cannot be further simplified.
2)
Here we have:
n = 5 (number of pots that Andy has)
(amount of soil (in pounds) that each pot can contain)
In order to find the amount of soil that Andy needs to fill all the pots, we have to multiply the number of pots (n) by the amount of soil that each pot can contain (s).
If we do so, we find:
Which can be rewritten as a mixed fraction as:
3)
Here we want to find the result of the following product:
In order to do so, we first have to rewrite each fraction as an improper fraction.
For the 1st fraction:
For the 2nd fraction:
Now we can finally find the product of the two fractions:
Where in the last step, we divide both the numerator and the denominator by 6.
Learn more about fractions:
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