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What is the solution to the inequality |2x + 3| < 7?

Answer's
4 < x < 10
–5 < x < 2
x < 4 or x > 10
x < –5 or x > 2

User Rajasekhar
by
8.0k points

1 Answer

6 votes

Answer:

The solution to the inequality |2x + 3| < 7 is:

  • -5 < x < 2

Explanation:

The given inequality contains an absolute value.

The absolute value of an expression is its positive numerical value.

Step 1

To solve the absolute value inequality, begin by isolating the absolute value on one side of the equation. (This has already been done for us).


\implies |2x+3| < 7

Step 2

Apply the absolute rule:


\boxed{\textsfu}

Therefore, we can create two inequalities:


\textsf{Inequality 1:} \quad 2x+3 < 7


\textsf{Inequality 2:} \quad 2x+3 > -7

Step 3

Solve both inequalities:


\boxed{\begin{aligned}\underline{\sf Inequality\;1}\\ \implies 2x+3&amp; < 7\\2x&amp; < 4\\x&amp; < 2\end{aligned}}
\boxed{\begin{aligned}\underline{\sf Inequality\;2}\\ \implies 2x+3&amp; > -7\\2x&amp; > -10\\x&amp; > -5\end{aligned}}

Step 4

Finally, merge the overlapping intervals:


-5 < x < 2

Solution

The solution to the inequality |2x + 3| < 7 is -5 < x < 2.

User Alan Kersaudy
by
7.7k points

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