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When an integer is subtracted from 8 times the next consecutive integer, the difference is -13 . Find the value of the greater integer.
Answer:

When an integer is subtracted from $8$ times the next consecutive integer, the difference is $-13$ . Find the value of the greater integer. $\newline$ Answer:

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Experimental probability

Full solution

Q. When an integer is subtracted from

8

times the next consecutive integer, the difference is

-13

. Find the value of the greater integer.

\newline

Answer:

Define Integers: Let's denote the first integer as $x$ . The next consecutive integer is $x + 1$ . According to the problem, $8$ times the next consecutive integer minus the first integer equals $-13$ . We can write this as an equation: $\newline$ $8(x + 1) - x = -13$
Distribute $8$ : Now, let's distribute the $8$ to both terms inside the parentheses: $8x + 8 - x = -13$
Combine Like Terms: Combine like terms by subtracting $x$ from $8x$ : $7x + 8 = -13$
Isolate Variable $x$ : Next, we need to isolate the variable $x$ . To do this, we subtract $8$ from both sides of the equation: $\newline$ $7x = -13 - 8$
Calculate Right Side: Now, calculate the right side of the equation: $7x = -21$
Divide by $7$ : To find the value of $x$ , divide both sides of the equation by $7$ : $\newline$ $x = \frac{-21}{7}$
Calculate $x$ : Calculate the division to find the value of $x$ : $x = -3$
Find Greater Integer: Since $x$ is the first integer, the next consecutive integer, which is the greater integer, is $x + 1$ . So we need to add $1$ to our value of $x$ to find the greater integer: $\newline$ Greater integer = $x + 1 = -3 + 1$
Calculate Greater Integer: Calculate the sum to find the value of the greater integer: Greater integer = $-2$

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