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Chapter 1: Problem 19

Let \(x\) represent the number. Use the given conditions to write an equation. Solve the equation and find the number. Nine times a number is 30 more than three times that number. Find the number.

Short Answer

Expert verified
The number is 5.

Step by step solution

01

Formulate the equation

The problem states that 'Nine times a number is 30 more than three times that number'. So we can write this statement as an equation like this: \(9x = 3x + 30\).
02

Rearrange the equation

To solve for \(x\), first isolate the \(x\) terms on one side of the equation and constant terms on the other. So, subtract \(3x\) from both sides which gives: \(9x - 3x = 30\), that simplifies to \(6x = 30\).
03

Solve the equation

Then, to find the value of \(x\), divide both sides of the equation by 6: \(x = 30/6\).

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Most popular questions from this chapter

In Exercises \(73-74\), use the method for solving quadratic inequalities to solve each higher-order polynomial inequality. $$ x^{3}+2 x^{2}-x-2 \geq 0 $$

In Exercises \(9-20,\) find each product and write the result in standard form. $$(8-4 i)(-3+9 i)$$

Explain the error in Exercises \(51-52\) \((\sqrt{-9})^{2}=\sqrt{-9} \cdot \sqrt{-9}=\sqrt{81}=9\)

In Exercises \(9-20,\) find each product and write the result in standard form. $$(2+3 i)^{2}$$

Explain how to multiply complex numbers and give an example.
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