Solving Multi-Step Equations | Math with Mr. J

Math with Mr. J・2 minutes read

The video tutorial teaches how to solve multistep equations using the distributive property and combining like terms, exemplified through solving two equations. Both examples demonstrate the step-by-step process of manipulating the equations and verifying the solutions for accuracy.

Insights

  • The tutorial effectively demonstrates how to solve multistep equations by applying the distributive property and combining like terms, illustrated through two detailed examples. In the first example, the equation \( x + 5(3x 4) = 12x + 4 \) is simplified step-by-step, ultimately revealing the solution \( x = 6 \), which is verified by substituting back into the original equation.
  • In the second example, the equation \( -9(M 2) + 7M = -10 \) showcases a similar approach, where distributing \(-9\) leads to \( -2M + 18 = -10 \). This is further simplified to find \( M = 14 \), with the solution also confirmed through substitution, reinforcing the importance of verification in solving equations.

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Recent questions

  • What is the distributive property in math?

    The distributive property is a fundamental algebraic principle that states that when you multiply a number by a sum, you can distribute the multiplication across each term in the sum. For example, in the expression \( a(b + c) \), you can apply the distributive property to rewrite it as \( ab + ac \). This property is essential for simplifying expressions and solving equations, as it allows for the expansion of terms and the combination of like terms, making it easier to isolate variables and find solutions.

  • How do I solve multistep equations?

    Solving multistep equations involves a systematic approach that includes applying the distributive property, combining like terms, and isolating the variable. Start by simplifying both sides of the equation, using the distributive property to eliminate parentheses. Next, combine any like terms to streamline the equation. After simplification, move the variable terms to one side and constant terms to the other side by performing inverse operations. Finally, isolate the variable by dividing or multiplying as necessary to find the solution. Always verify your solution by substituting it back into the original equation to ensure both sides are equal.

  • What are like terms in algebra?

    Like terms in algebra are terms that contain the same variable raised to the same power. For instance, in the expression \( 3x + 5x - 2y + 4y \), the terms \( 3x \) and \( 5x \) are like terms because they both contain the variable \( x \). Similarly, \( -2y \) and \( 4y \) are like terms as they both involve the variable \( y \). Combining like terms is a crucial step in simplifying algebraic expressions and solving equations, as it allows for the consolidation of terms to make calculations more manageable.

  • How do I verify my solution in equations?

    Verifying a solution in equations involves substituting the found value back into the original equation to check if both sides are equal. For example, if you solve for \( x \) and find \( x = 6 \), you would replace \( x \) in the original equation with 6 and perform the calculations on both sides. If both sides yield the same result, the solution is confirmed as correct. This step is essential in ensuring that no errors were made during the solving process and that the solution is valid within the context of the equation.

  • What is the importance of combining like terms?

    Combining like terms is crucial in algebra as it simplifies expressions and makes solving equations more efficient. By consolidating terms that share the same variable and exponent, you reduce the complexity of the equation, making it easier to isolate the variable and find a solution. This process not only streamlines calculations but also helps in organizing the equation, allowing for clearer understanding and manipulation of the mathematical relationships involved. Ultimately, combining like terms is a foundational skill that enhances problem-solving abilities in algebra and beyond.

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Summary

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Solving Multistep Equations with Examples

  • The video tutorial focuses on solving multistep equations, emphasizing the use of the distributive property, combining like terms, and handling variables on both sides of the equation. Two examples are provided to illustrate these concepts.
  • In the first example, the equation is \( x + 5(3x - 4) = 12x + 4 \). The distributive property is applied by multiplying 5 with both terms inside the parentheses, resulting in \( 5 \times 3x = 15x \) and \( 5 \times -4 = -20 \), leading to the equation \( x + 15x - 20 = 12x + 4 \).
  • After applying the distributive property, like terms \( x \) and \( 15x \) are combined to yield \( 16x - 20 = 12x + 4 \). The next step involves moving the variable terms to one side by subtracting \( 12x \) from both sides, resulting in \( 4 = 4x - 20 \).
  • To isolate \( x \), the equation is simplified by adding 20 to both sides, giving \( 4x = 24 \). The final step involves dividing both sides by 4, leading to the solution \( x = 6 \).
  • The solution is verified by substituting \( x = 6 \) back into the original equation. The left side calculates to \( 6 + 5(14) = 76 \) and the right side calculates to \( 12(6) + 4 = 76 \), confirming that both sides are equal.
  • The second example presented is \( -9(M - 2) + 7M = -10 \). The distributive property is used again, distributing \(-9\) to both \( M \) and \(-2\), resulting in \( -9M + 18 + 7M = -10 \).
  • After combining like terms, the equation simplifies to \( -2M + 18 = -10 \). To isolate \( M \), subtract 18 from both sides to get \( -2M = -28 \), and then divide by \(-2\) to find \( M = 14 \). This solution is also verified by substituting \( M = 14 \) back into the original equation, confirming the correctness of the solution.
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