Find three consecutive integers such that the largest is 3 less than twice the smallest

Mathematics

1 answer:

Nostrana [21]3 years ago

7 0

Answer:

The three consecutive integers are 5,6,7

Step-by-step explanation:

Let the three consecutive integers be represented as x,x+1,x+2

As per the requirement, largest integer is 3 less than twice the smallest.

=> x+ 2 = 2x -3

=> 2x -x = 2+3

=> x= 5

So the three integers are 5,6,7

Verification:

Largest integer = 7

Smallest integer = 5

2 * smallest integer - 3 = 2* 5 - 3 = 7

Largest integer is also 7.

So the required condition in the question is satisfied by these three integers.

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What is −13+2z=−56 Thanks

Zinaida [17]

<h3>Original Equation:</h3>

$-\frac{1}{3}+2z=-\frac{5}{6}$

<h3>Steps:</h3>

<em>*To solve for a variable, isolate the desired variable onto one side.</em>

Firstly, we want to add 1/3 to each side however -5/6 and 1/3 do not share the same denominator, and we want them to have that and we can do that by finding the LCD, or lowest common denominator. To find the LCD, list the multiples of 6 and 3 and the lowest multiple that they share is their LCD. In this case, their LCD is 6. Multiply -1/3 by 2/2:

$-\frac{1}{3}\times \frac{2}{2}=-\frac{2}{6}\\\\-\frac{2}{6}+2z=-\frac{5}{6}$

Now that we have common denominators, add both sides by 2/6:

$2z=-\frac{3}{6}\\\\2z=-\frac{1}{2}$

Next, you want to cancel out 2 to isolate z. Usually, one would divide both sides by 2, however remember that <u>dividing by a number is the same as multiplying by it's reciprocal.</u> To find a number's reciprocal, flip the numerator and denominator around. In this case, since 2 is a <em>whole number</em> this means that the denominator is 1. In this case: 2/1 would become 1/2. Multiply both sides by 1/2:

$\frac{1}{2}\times 2z= -\frac{1}{2}\times \frac{1}{2}\\\\z=-\frac{1}{4}$