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Chapter 3: Problem 513

In the following exercises, translate and solve. Eight less than \(y\) is \(-32\)

Short Answer

Expert verified
y = -24

Step by step solution

01

Identify the mathematical statement

Translate the phrase 'Eight less than y is -32' into a mathematical equation. This phrase means we need to subtract 8 from y. The equation becomes: y - 8 = -32
02

Isolate the variable

To solve for y, we need to isolate it on one side of the equation. Add 8 to both sides of the equation to cancel out the -8:y - 8 + 8 = -32 + 8which simplifies to: y = -24

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Key Concepts

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

translating verbal expressions to equations
Translating verbal expressions into equations is a crucial skill in prealgebra. It helps us turn word problems into solvable mathematical statements. Let's take the given exercise as an example: 'Eight less than y is -32.' Here, the phrase 'less than' indicates subtraction. Therefore, 'eight less than y' means we need to subtract 8 from some variable which we'll call y. So, the verbal expression 'Eight less than y is -32' translates to the equation:
y - 8 = -32

Breaking down verbal expressions into parts is essential. Look out for keywords like 'sum,' 'product,' 'difference,' and 'quotient' to understand what the mathematical operation will be.
isolating variables
Once we have the equation set up, the next step is isolating the variable. This means getting the variable by itself on one side of the equation
In the exercise, the equation is: y - 8 = -32

To isolate y, we need to eliminate the -8, which is attached to it by subtraction. We do this by performing the opposite operation. Adding 8 to both sides of the equation helps balance it out:
y - 8 + 8 = -32 + 8
This simplifies to: y = -24

Now y is isolated, and we've solved the equation. Learning to isolate variables is key because it lets us find unknown values in equations. A good tip is to always do the same operation on both sides of the equation to keep it balanced.
prealgebra word problems
Prealgebra word problems often involve translating a written statement into a mathematical equation and solving it. Let's revisit the given problem: 'Eight less than y is -32.'

To tackle such problems, follow these steps:
  • Identify important keywords.
  • Turn the keywords into mathematical operations.
  • Set up the equation based on the verbal statement.
  • Solve the equation by isolating the variable.

In our example:
  • 'Eight less than y' translates to 'y - 8'
  • 'is -32' translates to '= -32'
. Combining these gives us the equation y - 8 = -32.

By following these steps with any prealgebra word problem, you can easily set up and solve for the unknown variable. Practice makes perfect, so keep practicing to get more comfortable with these types of problems!

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Most popular questions from this chapter

In the following exercises, solve. $$ d-(-6)=-26 $$

In the following exercises, simplify each expression. $$ 45 \div(-3)-12 $$

In the following exercises, simplify each expression. $$ -3^{4} $$

In the following exercises, simplify each expression. $$ -3+6(-1+5) $$

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