Problem 72 - Elementary and Intermediate Algebra

Question

In each of Exercises \(71-78,\) match the phrase or sentence with the appropriate expression or equation from the column on the right. Five less than a number is nine._____ a) \(\frac{x}{y}+6\) b) \(2(x+y)=48\) c) \(\frac{1}{2} \cdot a \cdot b\) d) \(t+2=5\) e) \(a b-1=49\) f) \(2(m+n)\) g) \(3(t+5)\) h) \(x-5=9\)

Step-by-Step Solution

Answer

The phrase matches with option (h): \( x - 5 = 9 \).

Step 1: Understand the Phrase

The phrase is 'Five less than a number is nine.'

Step 2: Translate the Phrase to a Mathematical Expression

Identify the unknown number as a variable. Let's use the variable 'x' to represent the unknown number. The phrase 'five less than a number' can be translated to 'x - 5'.

Step 3: Write the Equation

The phrase says 'is nine,' which means we set up the equation by equating the expression from Step 2 to 9. Therefore, the equation becomes: \( x - 5 = 9 \)

Step 4: Match the Equation with the Given Options

Look for the equation that matches \( x - 5 = 9 \) among the given options. The correct match is option (h).

Key Concepts

algebraic expressions

Algebraic expressions are a key part of understanding and solving math problems. They consist of numbers, variables (like 'x' in this case), and operations (such as addition or subtraction). To master algebraic expressions, recognize the components of phrases to convert them into mathematical terms. For example, 'five less than a number' translates to 'x - 5'. The number five is subtracted from the unknown variable 'x'. Familiarizing yourself with such phrases will make it easier to write expressions whenever you encounter similar problems.

solving equations

Solving equations involves finding the value of the unknown variable that makes the equation true. Here, the equation is \( x - 5 = 9 \). To solve it, you'll need to isolate 'x' by performing operations that reverse the current ones.
Steps involved:

• Add 5 to both sides of the equation: \( x - 5 + 5 = 9 + 5 \).
• Simplify the expression: \( x = 14 \).
• So, the solution to the equation is \( x = 14 \).

Make sure to verify the solution by plugging 'x' back into the original equation to check if both sides are equal.

comprehension skills

Comprehending word problems is crucial for translating them into math. Start by identifying keywords and phrases that indicate mathematical operations.
For the given exercise:

• 'Five less than' signals a subtraction.
• 'A number' indicates an unknown variable.
• 'Is' points to an equality, implying both sides of the equation are balanced.

Breaking down the sentence helps you understand what it's asking for. Practice actively interpreting phrases, and over time, you'll better translate word problems into equations. Improving these skills will aid greatly in tackling various math problems effectively.