Solve for X: Finding Daily Rate in Expression 2x+4 = 24 Windows

Q: Why do I multiply (2x + 4) by 5?

Because (2x + 4) is the number of windows cleaned per day, and we need the total for 5 days. Think of it like: if you earn $20 per day, how much do you earn in 5 days? You multiply: 5 × $20.

Q: What does the distributive property do here?

The distributive property helps us expand 5(2x + 4) into 10x + 20. This removes the parentheses so we can solve the equation more easily.

Q: How can I check if x = 10 is correct?

Substitute back: If x = 10, then each day they clean 2(10) + 4 = 24 windows. Over 5 days: 5 × 24 = 120 windows total ✓

Q: What if I get confused about what 2x + 4 represents?

2x + 4 is an expression that tells us how many windows are cleaned each single day. It's not the total for all 5 days - that's why we multiply by 5!

Linear Equations with Algebraic Expressions

A window cleaner cleans 120 windows in 5 days.

Calculate $x$ given that each day they clean $2x+4$ windows.

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A window cleaner cleans 120 windows in 5 days.

Calculate $x$ given that each day they clean $2x+4$ windows.

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify variables and create an equation.
Step 2: Solve the equation for the unknown variable $x$ .

Now, let's work through each step:

Step 1: We know the window cleaner cleans $2x + 4$ windows each day. Over 5 days, the total windows cleaned can be expressed as:

$5 \times (2x + 4) = 120$

Step 2: Let's simplify and solve this equation:

First, distribute the 5 across the parenthesis:

$5 \times 2x + 5 \times 4 = 120$

Simplifying further gives:

$10x + 20 = 120$

Subtract 20 from both sides to isolate the term containing $x$ :

$10x = 100$

Now, divide both sides by 10 to solve for $x$ :

$x = 10$

Therefore, the solution to the problem is $x = 10$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Setup: Total work equals daily rate times number of days
Technique: Distribute multiplication: 5(2x + 4) = 10x + 20
Check: Substitute x = 10: 2(10) + 4 = 24 windows per day ✓

Common Mistakes

Avoid these frequent errors

Not setting up the equation correctly
Don't just solve 2x + 4 = 24 directly = ignores the 5-day period! This gives x = 10 by coincidence but misses the real relationship. Always multiply the daily rate by the number of days to get total work.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Why do I multiply (2x + 4) by 5?

Because (2x + 4) is the number of windows cleaned per day, and we need the total for 5 days. Think of it like: if you earn $20 per day, how much do you earn in 5 days? You multiply: 5 ×$ 20.

What does the distributive property do here?

The distributive property helps us expand 5(2x + 4) into 10x + 20. This removes the parentheses so we can solve the equation more easily.

How can I check if x = 10 is correct?

Substitute back: If x = 10, then each day they clean 2(10) + 4 = 24 windows. Over 5 days: 5 × 24 = 120 windows total ✓

What if I get confused about what 2x + 4 represents?

2x + 4 is an expression that tells us how many windows are cleaned each single day. It's not the total for all 5 days - that's why we multiply by 5!

Could there be other ways to solve this?

Yes! You could first find the daily rate: 120 ÷ 5 = 24 windows per day. Then solve 2x + 4 = 24 to get x = 10. Both methods work!

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