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Chapter 0: Problem 54

Solve each compound inequality. $$3 \leq 4 x-3<19$$

Short Answer

Expert verified
The solution for the compound inequality is \( 1.5 \leq x < 5.5 \)

Step by step solution

01

Split the compound inequality

Split the compound inequality into two separate inequalities: \( 3 \leq 4x - 3 \) and \( 4x - 3 < 19 \).
02

Solve the first inequality

We start solving \( 3 \leq 4x - 3 \) by first adding 3 to both sides to get \( 6 \leq 4x \). Then divide both sides by 4 to get the value of \( x \) for this inequality, which equals \( x \geq 1.5 \)
03

Solve the second inequality

We start solving \( 4x - 3 < 19 \) by first adding 3 to both sides to get \( 4x < 22 \). Then divide both sides by 4 to get the value of \( x \) for this inequality, which is \( x < 5.5 \)
04

Combine the results

Finally, to find the range of \( x \) that satisfies both inequalities, we bring together the individual results from Step 2 and Step 3. The intersection of those two inequalities gives us the final solution.

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Most popular questions from this chapter

Find \(b\) such that \(\frac{7 x+4}{b}+13=x\) will have a solution set given by \(\\{-6\\}\).

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