Four times a number decreased by four is between -40 and 88 . 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: -40 < 4x - 4 < 88Solve Left Inequality: First, we will solve the left part of the inequality: -40 < 4x - 4 We need to isolate the variable 'x', so we will add 4 to both sides of the inequality: -40 + 4 < 4x - 4 + 4 -36 < 4xIsolate Variable 'x': Now, we divide both sides of the inequality by 4 to solve for 'x': -36 ÷ 4 < 4x ÷ 4 -9 < xSolve Right Inequality: Next, we will solve the right part of the inequality: 4x - 4 < 88 Again, we will add 4 to both sides of the inequality: 4x - 4 + 4 < 88 + 4 4x < 92Combine Inequalities: We divide both sides of this inequality by 4 to solve for 'x': 4x ÷ 4 < 92 ÷ 4 x < 23Now we combine the two inequalities to find the interval for 'x': -9 < x < 23 This is the interval notation for the valid values of 'x'.

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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

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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 < 23Now 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'.