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What are the minimum and maximum values of t for which |t + 3| ≤ 2? minimum: maximum:

User BlueJapan
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1 Answer

15 votes
15 votes

It + 3I is called absolut value which means the value of t + 3 is always positive

So we will solve two inequalities


\begin{gathered} t+3\leq2 \\ -(t+3)\leq2 \end{gathered}

Let us solve the first one

Subtract from both sides 3


t+3-3\leq2-3
t\leq-1

Now we will solve the second one

We multiply the bracket by (-)


-t-3\leq2

Add 3 to both sides


\begin{gathered} -t-3+3\leq2+3 \\ -t\leq5 \end{gathered}

We will divide both sides by -1 the coefficient of t, but we must reverse the sign of the inequality because 2 < 3 if we divide both sides by -1 it will be -2 < -3 which is wrong -2 > -3, so

When you multiply or divide an inequality by negative number you must reverse the sign of the inequality


\begin{gathered} -1(-t)\ge-1(5) \\ t\ge-5 \end{gathered}

Now we will write the both inequalities togather


-5\leq t\leq-1

The minimum value is -5

The maximum value is -1

User Slateboard
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