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Four times a number decreased by $4$ is between $-40$ and $88$ . $\newline$ Find the interval for valid values. (The answer should be in interval notation.)

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Mean, variance, and standard deviation of binomial distributions

Full solution

Q. Four times a number decreased by

4

is between

-40

and

88

.

\newline

Find the interval for valid values. (The answer should be in interval notation.)

Define Unknown Number: Let's denote the unknown number as ' $x$ '. The problem states that four times a number decreased by four is between $-40$ and $88$ . We can write this as an inequality: $\newline$ $-40 < 4x - 4 < 88$
Solve Left Inequality: First, we will solve the left part of the inequality: $\newline$ $-40 < 4x - 4$ $\newline$ We need to isolate the variable $x$ , so we will add $4$ to both sides of the inequality: $\newline$ $-40 + 4 < 4x - 4 + 4$ $\newline$ $-36 < 4x$
Isolate Variable 'x': Now, we divide both sides of the inequality by $4$ to solve for 'x': $\newline$ $-36 \div 4 < 4x \div 4$ $\newline$ $-9 < x$
Solve Right Inequality: Next, we will solve the right part of the inequality: $\newline$ $4x - 4 < 88$ $\newline$ Again, we will add $4$ to both sides of the inequality: $\newline$ $4x - 4 + 4 < 88 + 4$ $\newline$ $4x < 92$
Combine Inequalities: We divide both sides of this inequality by $4$ to solve for 'x': $\newline$ $4x \div 4 < 92 \div 4$ $\newline$ $x < 23$
Combine Inequalities: We divide both sides of this inequality by $4$ to solve for 'x': $\newline$ $4x \div 4 < 92 \div 4$ $\newline$ $x < 23$ Now we combine the two inequalities to find the interval for 'x': $\newline$ $-9 < x < 23$ $\newline$ This is the interval notation for the valid values of 'x'.

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