Pre-Algebra: Solving Equations
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Questions and Answers

Solve the equation 2x - 5 = 11. Check your solution to ensure it is true.

x = 8; Yes, 2(8) - 5 = 11.

Solve the equation 3/4 x = 9/2. Show all work and write yes or no if the solution is true.

x = 6; Yes, 3/4 (6) = 9/2.

Solve the equation x/2 + 3 = 7. Check your solution to ensure it is true.

x = 8; Yes, 8/2 + 3 = 7.

Solve the equation 2x - 3 = 5. Show all work and write yes or no if the solution is true.

<p>x = 4; Yes, 2(4) - 3 = 5.</p> Signup and view all the answers

Solve the equation x/4 - 2 = 3. Check your solution to ensure it is true.

<p>x = 20; Yes, 20/4 - 2 = 3.</p> Signup and view all the answers

What is the key concept that defines a fraction, and what are the two parts that make up a fraction?

<p>A fraction represents a part of a whole and consists of a numerator (top number) and a denominator (bottom number).</p> Signup and view all the answers

When adding or subtracting fractions, what method can be used to find a common denominator?

<p>The least common multiple (LCM) method can be used to find a common denominator.</p> Signup and view all the answers

What is the process for multiplying fractions, and how does it differ from adding or subtracting fractions?

<p>To multiply fractions, multiply the numerators and multiply the denominators. This is different from adding or subtracting fractions, which requires a common denominator.</p> Signup and view all the answers

What is the goal of simplifying fractions, and how is it achieved?

<p>The goal of simplifying fractions is to find an equivalent fraction in its simplest form. This is achieved by dividing both the numerator and denominator by their greatest common divisor (GCD).</p> Signup and view all the answers

What is the coordinate plane, and what is the purpose of the x-axis and y-axis?

<p>The coordinate plane is a grid with a horizontal x-axis and a vertical y-axis. The x-axis and y-axis provide a framework for graphing points and visualizing relationships between variables.</p> Signup and view all the answers

What is the slope-intercept form of a linear equation, and what do the variables m and b represent?

<p>The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.</p> Signup and view all the answers

What is the definition of a solution to an equation, and how can you check if a solution is true?

<p>A solution to an equation is a value of the variable that makes the equation true. You can check if a solution is true by plugging it back into the original equation.</p> Signup and view all the answers

What is the order of operations when working with equations, and why is it important?

<p>The order of operations is PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). It is important to follow this order to ensure accurate calculations and solutions.</p> Signup and view all the answers

What is the purpose of inverse operations when solving equations, and how do you use them to isolate the variable?

<p>Inverse operations are used to isolate the variable in an equation. You can add, subtract, multiply, or divide both sides of the equation by the same value to isolate the variable.</p> Signup and view all the answers

What is the difference between solving linear equations and multi-step equations, and how do you approach each?

<p>Linear equations have one variable and one solution, whereas multi-step equations require more than one step to solve. To solve multi-step equations, follow the order of operations and use inverse operations to isolate the variable.</p> Signup and view all the answers

Study Notes

Solving Equations in Pre-Algebra

  • Solving equations involve working with negative numbers, division, and multiplication.
  • Equations can also involve fractions, which require special care when solving.
  • Equations typically involve one variable, which needs to be solved for.
  • To verify a solution, plug the given solution back into the original equation to determine if it makes the equation true.
  • Combining like terms often requires creating new equations to simplify the original equation.

Fractions

Key Concepts

  • A fraction represents a part of a whole, consisting of a numerator (top number) and a denominator (bottom number) that cannot be zero.
  • The numerator and denominator of a fraction are separated by a horizontal line or a diagonal slash.

Operations with Fractions

  • To add or subtract fractions, a common denominator is required, which can be found using the least common multiple (LCM) method.
  • When multiplying fractions, the numerators and denominators are multiplied separately, resulting in a new fraction.
  • To divide fractions, invert the second fraction and multiply, which is equivalent to flipping the second fraction and multiplying.

Simplifying Fractions

  • Simplifying fractions involves dividing both the numerator and denominator by their greatest common divisor (GCD) to find an equivalent fraction in simplest form.

Graphing

Key Concepts

  • A coordinate plane consists of a grid with a horizontal x-axis and a vertical y-axis.
  • Points on the coordinate plane are represented by ordered pairs (x, y), where x is the horizontal distance and y is the vertical distance from the origin.

Graphing Lines

  • The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
  • The slope of a line represents the rise over run (m = Δy / Δx), and it can be positive, negative, zero, or undefined.
  • The x-intercept is the point where the line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis.

Solving Equations

Key Concepts

  • Equations are statements that two expressions are equal, and solving them involves finding the value of the variable that makes the equation true.
  • Solutions to equations can be checked by plugging them back into the original equation.

Linear Equations

  • Linear equations involve one variable and have one solution, which can be found by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
  • To solve linear equations, isolate the variable by performing inverse operations and combining like terms to simplify the equation.

Solving Multi-Step Equations

  • When solving multi-step equations, follow the order of operations (PEMDAS) when working with parentheses.
  • Use inverse operations to isolate the variable, and combine like terms to simplify the equation.

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Practice solving equations in pre-algebra, including equations with negative numbers, division, multiplication, and fractions. Learn to verify solutions and combine like terms.

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