Problem 127
Question
In the following exercises, translate to an algebraic expression and simplify if possible. the sum of 3 and -15 , increased by 7
Step-by-Step Solution
Verified Answer
-5
1Step 1: Identify the First Expression
The exercise asks for the sum of 3 and -15. Write this as a mathematical expression: 3 + (-15)
2Step 2: Simplify the First Expression
Simplify the sum, 3 + (-15) = -12
3Step 3: Identify the Next Operation
The simplified result from the first part, -12, needs to be increased by 7. Write this as an expression: -12 + 7
4Step 4: Simplify the Final Expression
Simplify the sum to get the final result, -12 + 7 = -5
Key Concepts
Simplifying ExpressionsSum of NumbersIdentifying OperationsAlgebraic Translation
Simplifying Expressions
One of the essential skills in algebra is simplifying expressions. When you simplify an expression, you make it easier to work with, often by combining like terms or reducing it to its simplest form.
For example, in the exercise, we first encounter the expression, 3 + (-15). When simplified, it becomes -12. Simplifying step by step prevents errors and makes solving more manageable.
Think of simplifying as cleaning up a messy room—everything gets organized, and it's easier to find what you need.
For example, in the exercise, we first encounter the expression, 3 + (-15). When simplified, it becomes -12. Simplifying step by step prevents errors and makes solving more manageable.
Think of simplifying as cleaning up a messy room—everything gets organized, and it's easier to find what you need.
Sum of Numbers
The term 'sum' in mathematics signifies adding two or more numbers together.
In the exercise, you are asked to find the sum of 3 and -15.
Recognizing words like 'sum' helps you decode what mathematical operation to perform.
Also, understand that adding a negative number is like subtracting its positive counterpart, helping you understand the operation better.
Points to remember:
In the exercise, you are asked to find the sum of 3 and -15.
Recognizing words like 'sum' helps you decode what mathematical operation to perform.
Also, understand that adding a negative number is like subtracting its positive counterpart, helping you understand the operation better.
Points to remember:
- 'Sum' means addition.
- Adding a positive number increases the total.
- Adding a negative number decreases the total.
Identifying Operations
Identifying operations in a problem is like finding the ingredients in a recipe.
In our example, you first identify that you need to add 3 and -15. This operation (3 + (-15)) results in -12.
Next, you identify that the result should be increased by 7, or -12 + 7. Identifying each required operation ensures that you handle each step correctly.
Words to look for:
In our example, you first identify that you need to add 3 and -15. This operation (3 + (-15)) results in -12.
Next, you identify that the result should be increased by 7, or -12 + 7. Identifying each required operation ensures that you handle each step correctly.
Words to look for:
- 'Sum' means addition.
- 'Difference' means subtraction.
- 'Product' means multiplication.
- 'Quotient' means division.
Algebraic Translation
Algebraic translation involves turning words into mathematical expressions. Think of it as translating a sentence from one language to another.
In our exercise, 'the sum of 3 and -15, increased by 7' turns into the expression 3 + (-15) + 7.
Each phrase in the sentence corresponds to a mathematical operation. You break it down and then solve it.
Key Tips for Algebraic Translation:
With practice, translating words to algebraic expressions will become second nature.
In our exercise, 'the sum of 3 and -15, increased by 7' turns into the expression 3 + (-15) + 7.
Each phrase in the sentence corresponds to a mathematical operation. You break it down and then solve it.
Key Tips for Algebraic Translation:
- Identify keywords ('sum,' 'difference,' etc.).
- Translate phrases step-by-step.
- Simplify expressions as you go.
With practice, translating words to algebraic expressions will become second nature.
Other exercises in this chapter
Problem 125
In the following exercises, evaluate each expression. \(3 x^{2}-4 x y+2 y^{2}\) when \(x=-2, y=-3\)
View solution Problem 126
In the following exercises, evaluate each expression. \(4 x^{2}-x y+3 y^{2}\) when \(x=-3, y=-2\)
View solution Problem 128
In the following exercises, translate to an algebraic expression and simplify if possible. the sum of -8 and -9 , increased by 23
View solution Problem 129
In the following exercises, translate to an algebraic expression and simplify if possible. (a) the difference of 10 and -18 (b) subtract 11 from -25
View solution