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Chapter 2: Problem 149

Translate to an equation and then solve. \(j\) divided by -20 is equal to \(-80 .\)

Short Answer

Expert verified
j = 1600

Step by step solution

01

Translate the Problem into an Equation

Express the given statement 'j divided by -20 is equal to -80' as an algebraic equation. In this case, the translation is \(\frac{j}{-20} = -80\).
02

Isolate the Variable

To solve for \(j\), isolate the variable by multiplying both sides of the equation by -20. This step will look like: \(\frac{j}{-20} \times -20 = -80 \times -20\).
03

Simplify Both Sides

Perform the multiplication to simplify both sides of the equation: \(j = 1600\).

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Key Concepts

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

Translating Word Problems to Equations
Word problems can sometimes feel tricky. The key to solving them is translating the words into mathematical equations. Let鈥檚 break down the sentence:
  • 'j divided by -20' means we take the variable j and divide it by -20. Mathematically, it looks like this: \(\frac{j}{-20}\).
  • 'Is equal to' translates to the '=' sign.
  • Finally, '-80' is already in mathematical terms.
Combining these pieces together, we get: \(\frac{j}{-20} = -80\). Remember that translating word problems step-by-step can simplify complex problems into solvable equations.
Isolating Variables
Once we have the equation generally formulated, the next step is to isolate the variable. In our example, the variable to isolate is \(j\).
To isolate \(j\), we move everything else on the same side of the equation to the other side. Here鈥檚 how:
  • We see that \(j\) is being divided by -20. To reverse this, we do the opposite operation, which is multiplication.
  • Multiply both sides of the equation by -20: \(\frac{j}{-20} \times -20 = -80 \times -20\).
By multiplying both sides by -20, we cancel out the \( -20 \) on the left. And, we get: \( j = -80 \times -20\).
Isolating variables effectively helps in moving one step closer to solving the equation.
Multiplication and Division of Integers
When solving equations, handling integers correctly is crucial.
In our problem, after isolating the variable \(j\), we need to multiply integers. Here鈥檚 a review:
  • \( -80 \times -20 = 1600 \) happens because a negative times a negative gives a positive result.
  • When dealing with multiplication or division of integers, remember these rules:
    • Positive \( \times \) Positive = Positive
    • Negative \( \times \) Negative = Positive
    • Positive \( \times \) Negative = Negative
    • Negative \( \times \) Positive = Negative
With these rules in mind, the solution becomes clearer. Multiply both sides to get \( j = 1600\).

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Most popular questions from this chapter

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$u+25>21$$

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$6 h-4(h-1) \leq 7 h-11$$

Graph each inequality on the number line and write in interval notation. (a) \(\quad x \geq-4\) (b) \(\quad x<2.5\) (c) \(x>-\frac{3}{2}\)

Taylor has $$\$ 2.00$$ in dimes and pennies. The number of pennies is 2 more than the number of dimes. Solve the equation \(0.10 d+0.01(d+2)=2\) for \(d\), the number of dimes.

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