Chapter 10: Q17. (page 528)

Solve the inequality $5^{2 x + 3} \leq 125$ . Check your solution.

Short Answer

Expert verified

The solution for the given inequality is $x \leq 0$ .

Step by step solution

Step 1. Write down the given expression.

The given inequality is $5^{2 x + 3} \leq 125$ .

Step 2. Simplify the equation.

The given inequality $5^{2 x + 3} \leq 125$ is solved as:

$\begin{array}{l} 5^{2 x + 3} \leq 125.... (Given) \\ {(5)}^{2 x + 3} \leq {(5)}^{3} \\ 2 x + 3 \leq 3 \\ 2 x \leq 0 \\ x \leq 0 \end{array}$

Step 3. Verify the result for obtained value.

Plugging $x = 0$ in given inequality and verify the result.

$\begin{array}{l} 5^{2 x + 3} \leq 125.... (Given) \\ 5^{2 (0) + 3} \leq 125.... (Plugging x = 0) \\ 5^{3} \leq 125 \\ 125 = 125.... (True) \end{array}$

Hence the solution is verified for $x = 0$ .

Step 4. Conclusion.

The solution for the given inequality is $x \leq 0$ .

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Solve the inequality $5^{2 x + 3} \leq 125$ . Check your solution.

Short Answer

Step by step solution

Step 1. Write down the given expression.

Step 2. Simplify the equation.

Step 3. Verify the result for obtained value.

Step 4. Conclusion.

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Solve the inequality 52x+3≤125. Check your solution.

Short Answer

Step by step solution

Step 1. Write down the given expression.

Step 2. Simplify the equation.

Step 3. Verify the result for obtained value.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Applied Mathematics

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Solve the inequality $5^{2 x + 3} \leq 125$ . Check your solution.