Solve for X in Trapezoid: Perimeter = 32.5 with Expressions x+2, 3x+1.5

Q: What does 'combine like terms' mean exactly?

Like terms have the same variable with the same exponent. In this problem: x + x + x + 3x = 6x (all x terms) and 2 + (-1) + 1.5 = 2.5 (all constant terms).

Q: Why is the perimeter given as 32.5 instead of a whole number?

Real-world measurements often include decimals! The decimal 1.5 in the expression 3x+1.5 creates the decimal result. This is completely normal in geometry problems.

Q: How do I check if x = 5 is really correct?

Substitute x = 5 into each expression: Top: 5+2 = 7Right: 5Left: 5-1 = 4Bottom: 3(5)+1.5 = 16.5Then add: 7 + 5 + 4 + 16.5 = 32.5 ✓

Perimeter Equations with Algebraic Expressions

Calculate X in the trapezoid below.

Perimeter = P

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate X in the trapezoid below.

Perimeter = P

Step-by-step solution

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

Step 1: Set up the equation using the given lengths and the perimeter formula.
Step 2: Simplify and solve the equation for $x$ .

Step 1: The equation for the perimeter using the side lengths is:

x + 2 + x + x - 1 + 3x + 1.5 = 32.5

Combine like terms:

6x + 2.5 = 32.5

Step 2: Solve for $x$ by isolating it:

Subtract 2.5 from both sides:

6x = 30

Divide by 6:

x = 5

Therefore, the solution to the problem is $x = 5$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Perimeter Formula: Add all four sides of the trapezoid together
Technique: Combine like terms: 6x + 2.5 = 32.5
Check: Substitute x = 5: 7 + 5 + 4 + 16.5 = 32.5 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to combine like terms before solving
Don't solve (x+2) + x + (x-1) + (3x+1.5) = 32.5 without simplifying first = messy algebra! This leads to confusion and calculation errors. Always combine like terms to get 6x + 2.5 = 32.5 before isolating x.

Practice Quiz

Test your knowledge with interactive questions

Given the trapezoid:

What is the area?

FAQ

Everything you need to know about this question

How do I know which expressions go with which sides?

Look at the diagram carefully! Each side of the trapezoid is labeled with its algebraic expression. The top side is x+2, right side is x, bottom side is 3x+1.5, and left side is x-1.

What does 'combine like terms' mean exactly?

Like terms have the same variable with the same exponent. In this problem: x + x + x + 3x = 6x (all x terms) and 2 + (-1) + 1.5 = 2.5 (all constant terms).

Why is the perimeter given as 32.5 instead of a whole number?

Real-world measurements often include decimals! The decimal 1.5 in the expression 3x+1.5 creates the decimal result. This is completely normal in geometry problems.

Can I solve this without combining like terms first?

Technically yes, but it's much harder! You'd have to keep track of many more terms. Always simplify first - it prevents mistakes and makes the algebra cleaner.

How do I check if x = 5 is really correct?

Substitute x = 5 into each expression:

Top: 5+2 = 7
Right: 5
Left: 5-1 = 4
Bottom: 3(5)+1.5 = 16.5

Then add: 7 + 5 + 4 + 16.5 = 32.5 ✓

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