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Setting This Equal to 150: A Simple Guide to Solving Linear Equations
Setting This Equal to 150: A Simple Guide to Solving Linear Equations
Understanding how to set an expression equal to 150 is essential for mastering algebra and solving real-world problems. Whether you're working on word problems, budgeting, or scientific calculations, knowing how to set and solve equations—like something = 150—is a foundational skill. In this guide, we’ll explore what it means to set an expression equal to 150, how to solve such equations, and real-life applications that illustrate their importance.
Understanding the Context
What Does It Mean to Set an Expression Equal to 150?
When you see an equation like set this equal to 150, you’re dealing with a statement of equivalence. The goal is to isolate the variable to find what number (or expression) makes the entire left side equal exactly 150. This setup appears frequently in math and applied disciplines because 150 often represents a target, limit, or benchmark value.
For example:
- Set the expression \( x + 45 \) equal to 150.
- Find the value of \( y \) such that \( 3y = 150 \).
In both cases, the equation expression = 150 asks, “What value does X need to take so that when plugged into this expression, the result is 150?”
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Key Insights
How to Set and Solve Equations Equal to 150
Step 1: Write the Equation
Start by expressing the relationship algebraically. For instance:
\[
x + 45 = 150
\]
Step 2: Isolate the Variable
To solve for \( x \), subtract 45 from both sides:
\[
x + 45 - 45 = 150 - 45
\]
\[
x = 105
\]
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Practical Examples & Applications
1. Budgeting:
Imagine you have $150 to spend on snacks and drinks. If drinks cost $45, how much can you spend on snacks?
Set up the equation:
\[
\ ext{Snack money} + 45 = 150
\]
\[
\ ext{Snack money} = 150 - 45 = 105
\]
You can buy snacks with $105.
2. Science & Measurement:
Suppose a recipe requires a total mixture volume of 150 mL, and 45 mL is already liquid. How much more solid or dry ingredient do you need?
\[
x + 45 = 150 \implies x = 105 \ ext{ mL}
\]
Tips for Quick Solving
- Always aim to isolate the variable by undoing addition/subtraction with inverse operations.
- Balance both sides of the equation to maintain equality.
- Check your solution by substituting back into the original expression.
If \( x = 105 \), then:
\[
105 + 45 = 150 \quad \ ext{(True!)}
\]
Why Learning This Matters
Setting an expression equal to 150 is not just an abstract exercise. It builds critical thinking for:
