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Chapter 2: Problem 28

Solve each equation, and check the solution. $$ -9 x=36 $$

Short Answer

Expert verified
The solution is x = -4.

Step by step solution

01

Isolate the variable

To solve for the variable, divide both sides of the equation by -9. The goal is to get x by itself on one side of the equation. \tewline \tewline \t\[-9x = 36\] \tewline \tewline \tDivide both sides by -9:\tewline \tewline \t\[ x = \frac{36}{-9} \]
02

Simplify

Simplify the right-hand side of the equation: \tewline \tewline \t\[ x = -4 \]
03

Check the solution

Substitute x back into the original equation to verify the solution: \tewline \tewline \t\[-9(-4) = 36\] \tewline \tewline \tSince \[ 36 = 36\] holds true, the solution is correct.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolate the variable
To solve any equation, one of the core steps is to isolate the variable. This means getting the variable鈥攍ike \( x \)鈥攁lone on one side of the equation. In this exercise, the given equation is:

To isolate \( x \) from \( -9x = 36 \), you need to get rid of the coefficient (the number multiplying the variable). The current coefficient is -9. You can do this by dividing both sides of the equation by -9:

  • The equation becomes \( x = \frac{36}{-9} \).


    • Dividing each side by -9, which is the opposite operation of multiplication, leaves \( x \) on one side of the equation.
Simplify
Once you've isolated the variable, the next step is to simplify your result. Simplification means reducing the equation to its simplest form. For our exercise:

  • We have \( x = \frac{36}{-9} \).


    • When you divide 36 by -9, you get -4. So, the simplified form of the equation is:

    • \( x = -4 \).


      • Make sure your fraction or result is completely simplified. This practice makes the solution clearer and easier to understand.
Check the solution
The last essential step is to check your solution. Checking ensures that your solution is correct and satisfies the original equation. You do this by substituting your found value back into the original equation. For our exercise:

Let's substitute \(-4\) back into the original equation \(-9x = 36\):
  • Substitute \( x = -4 \).
    • \(-9(-4) = 36 \)


      • -9 times -4 equals 36, which matches the original right-hand side of the equation. Therefore, the solution \( x = -4 \) is correct.
      • Seeing that \(36 = 36 \) holds true confirms our solution is valid.


        • Always take this extra verification step to make sure your answer works within the context of the original problem.

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Most popular questions from this chapter

Graph the solution set, and write it using interval notation \(-12 \leq \frac{3}{7} x+2 \leq-4\)

Solve each problem. In each case, give an equation using \(x\) as the variable and give the answer. See Examples 1 and \(2 .\) The sum of a number and 9 is \(-26 .\) What is the number?

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