49-6(4x-7) Pls Help Me. If you're struggling to understand the algebraic expression 49 - 6(4x - 7) and how to simplify or solve it, you're not alone. Algebra can be challenging at first, but with the right approach and clear explanations, you can master these types of problems. In this comprehensive guide, we'll explore the step-by-step process to simplify the expression, solve for x, and understand the concepts involved. Whether you're a student preparing for tests or someone brushing up on algebra skills, this article aims to provide clarity and confidence.
Understanding the Expression 49 - 6(4x - 7)
Before diving into solving or simplifying the expression, it's important to understand its components.
Breaking Down the Expression
- 49: A constant term.
- 6(4x - 7): A product involving a coefficient (6) and a binomial (4x - 7).
- The expression involves combining constants and variables, along with applying the distributive property.
What is the Goal?
- Simplify the expression as much as possible.
- Solve for the variable x if an equation is given (e.g., set equal to a number).
- Understand the algebraic principles involved, including distribution and combining like terms.
Step-by-Step Simplification of 49 - 6(4x - 7)
Let's walk through the process to simplify this expression.
1. Apply the Distributive Property
The distributive property states that: \[ a(b + c) = ab + ac \] Applying this to \( -6(4x - 7) \): \[ -6 \times 4x + (-6) \times (-7) = -24x + 42 \]2. Rewrite the Expression
Substitute the distributed terms back into the original expression: \[ 49 - 6(4x - 7) = 49 - 24x + 42 \]3. Combine Like Terms
Constants 49 and 42 can be combined: \[ 49 + 42 = 91 \] Resulting in: \[ 91 - 24x \]4. Final Simplified Expression
The simplified form of 49 - 6(4x - 7) is: \[ \boxed{91 - 24x} \]Solving Equations Involving 49 - 6(4x - 7)
Often, you'll encounter problems where this expression is set equal to a number, and you'll need to find the value of x.
Example Equation
Suppose you are asked to solve: \[ 49 - 6(4x - 7) = 0 \]Step-by-Step Solution
Step 1: Simplify the expression
As already done, rewrite:
\[ 91 - 24x = 0 \]
Step 2: Isolate the variable term
Subtract 91 from both sides:
\[ -24x = -91 \]
Step 3: Solve for x
Divide both sides by -24:
\[ x = \frac{-91}{-24} \]
Step 4: Simplify the fraction
Since both numerator and denominator are negative:
\[ x = \frac{91}{24} \]
Result:
\[ \boxed{x = \frac{91}{24}} \]
Additional Tips for Solving Similar Algebraic Expressions
To enhance your understanding and problem-solving skills, here are some key tips:
Key Points to Remember
- Always apply the distributive property first when parentheses are involved.
- Combine like terms carefully, paying attention to signs.
- Keep track of positive and negative signs throughout calculations.
- When solving equations, isolate the variable step by step.
- Simplify fractions when possible to get the most reduced answer.
Common Mistakes to Avoid
- Forgetting to distribute the negative sign outside parentheses.
- Incorrectly combining constants or variables.
- Dividing by zero in equations (which is undefined).
- Mixing up signs, especially with negative coefficients.
Practical Applications of 49 - 6(4x - 7)
Understanding how to manipulate expressions like 49 - 6(4x - 7) isn't just an academic exercise; it has real-world applications.
Real-World Scenarios
- Financial calculations: Calculating profit or loss after deductions.
- Physics: Determining displacement or force with algebraic formulas.
- Engineering: Solving for variables in design equations.
- Statistics: Simplifying formulas involving variables and constants.
Example Application
Suppose a business has a revenue formula: \[ R = 49 - 6(4x - 7) \] where \( x \) could represent the number of units sold. Simplifying the expression helps determine revenue based on units sold.Practice Problems to Strengthen Your Skills
Engaging with practice problems is essential to mastering algebra.
- Simplify: \( 49 - 6(3x + 2) \)
- Solve: \( 49 - 6(4x - 7) = 91 \)
- Find x when: \( 49 - 6(4x - 7) = 0 \)
- Express \( 49 - 6(4x - 7) \) in terms of x and evaluate for \( x=2 \)
- Rewrite the expression as an equivalent linear expression
Answers:
- \( 49 - 18x - 12 = 37 - 18x \)
- \( 91 - 24x = 91 \Rightarrow -24x=0 \Rightarrow x=0 \)
- As shown above, \( x=\frac{91}{24} \)
- \( 91 - 24(2) = 91 - 48=43 \)
- The linear expression is \( 91 - 24x \)
Conclusion: Mastering Algebraic Expressions Like 49 - 6(4x - 7)
Understanding and solving algebraic expressions such as 49 - 6(4x - 7) is fundamental to progressing in mathematics. By applying the distributive property, combining like terms, and solving for variables systematically, you can confidently tackle similar problems. Remember to practice regularly, double-check your work, and keep a clear step-by-step approach. With dedication and practice, algebra will become an easier and more intuitive part of your mathematical toolkit.
Additional Resources for Learning Algebra
- Online tutorials and videos
- Algebra textbooks and workbooks
- Educational apps and interactive platforms
- Tutoring services and study groups
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