Example Question - distance from zero
Here are examples of questions we've helped users solve.
Absolute Value Expression Evaluation
La expresión mostrada en la imagen es: - | -7 | Primero vamos a determinar el valor absoluto de -7. El valor absoluto de un número es la distancia que hay desde ese número hasta el 0 en la recta numérica, sin considerar la dirección. Por lo tanto, el valor absoluto de -7 es 7, ya que está a 7 unidades de distancia del 0. Ahora que tenemos | -7 | = 7, sustituimos este valor en la expresión inicial: - | -7 | = -7 Por lo tanto, el valor de la expresión es -7.
Solving Inequalities with Absolute Value
To solve the inequality \( |t - 75| \leq 15 \), we need to split it into two separate inequalities, because the absolute value of a number is the distance from zero on the number line, and it can be expressed as the value being either greater than or equal to 0 or less than or equal to 0. The two cases for \( |t - 75| \leq 15 \) are: 1. \( t - 75 \leq 15 \) 2. \( -(t - 75) \leq 15 \) or equivalently \( t - 75 \geq -15 \) For the first case (1): \( t - 75 \leq 15 \) Adding 75 to both sides of the inequality gives us: \( t \leq 90 \) For the second case (2): \( t - 75 \geq -15 \) Adding 75 to both sides of this inequality gives us: \( t \geq 60 \) So, the solution to \( |t - 75| \leq 15 \) is the set of values of \( t \) that satisfy both conditions: \( 60 \leq t \leq 90 \) This means that the value of \( t \) is between 60 and 90, inclusive.
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