Solving One-Step Equations

One-Step Equations

• An equation is a mathematical statement showing that two expressions have the same value.
• A one-step equation is an equation containing a variable where one operation must be performed to find the value of that variable.

Solving One-Step Equations

• The goal is to notice which operation is being performed and use the inverse operation to solve.
• Examples:
  • x + 3 = 6: subtract 3 from both sides to solve for x.
  • 2x = 8: divide both sides by 2 to solve for x.

One-Step Equations with Fractions

• A fraction is a number in the form of a/b, where a and b are whole numbers.
• In a fraction, a is called the numerator, and b is called the denominator.

Fractions Operations

• Adding Fractions:
  • If two fractions have the same denominator, add the numerators and keep the denominator.
  • If fractions do not have the same denominator, find the least common multiple of the denominators and multiply the top and bottom of each fraction by a number to create a common denominator.
• Subtracting Fractions:
  • Once a common denominator is achieved, subtract the numerators and keep the denominators the same.
• Multiplying Fractions:
  • Multiply the numerators and multiply the denominators.
• Dividing Fractions:
  • Divide the numerators and divide the denominators.
  • Dividing by a fraction is the same as multiplying by its reciprocal.

Solving One-Step Equations with Fractions

• Recognize the operation in the equation and use the inverse operation to solve.
• Example 1:
  • x - 1/2 = 3/4: add 1/2 to both sides and find a common denominator to add the fractions.
• Example 2:
  • x/2 = 3/4: multiply both sides by 2 to eliminate the fraction on the left side.
  • Divide both sides by 3/4, which is the same as multiplying by its reciprocal, 4/3.