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Solve the inequality:

[tex]\[ |3x| + 4 \ \textless \ 10 \][/tex]


Sagot :

Certainly! Let's solve the inequality [tex]\( |3x| + 4 < 10 \)[/tex] step by step.

1. Start with the given inequality:
[tex]\[ |3x| + 4 < 10 \][/tex]

2. Isolate the absolute value term:
[tex]\[ |3x| + 4 - 4 < 10 - 4 \][/tex]
Simplifying, we get:
[tex]\[ |3x| < 6 \][/tex]

3. Understand the meaning of the absolute value inequality:
The inequality [tex]\( |3x| < 6 \)[/tex] means that the expression inside the absolute value [tex]\(3x\)[/tex] lies between [tex]\(-6\)[/tex] and [tex]\(6\)[/tex].

4. Write the compound inequality:
[tex]\[ -6 < 3x < 6 \][/tex]

5. Solve for [tex]\(x\)[/tex] by dividing every part of the inequality by 3:
[tex]\[ \frac{-6}{3} < \frac{3x}{3} < \frac{6}{3} \][/tex]
Simplifying each term, we get:
[tex]\[ -2 < x < 2 \][/tex]

Thus, the solution to the inequality [tex]\( |3x| + 4 < 10 \)[/tex] is:
[tex]\[ -2 < x < 2 \][/tex]

This means that [tex]\(x\)[/tex] must lie within the interval [tex]\((-2, 2)\)[/tex].
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