solving equations by clearing fractions

Solve the equation: 2x - (3x + 1) = 2(x + 4)

• x = 2

• x = 1

• x = -3

• x = 3

What is the least common denominator (LCD)?

• The largest multiple that is common to the denominators of two or more fractions.

• The smallest multiple that is common to the denominators of two or more fractions.

• The sum of the denominators of two or more fractions.

• The difference between the denominators of two or more fractions.

What is the first step in solving an equation with fractions?

• Identify the least common denominator (LCD) of all the fractions in the equation.

• Multiply all terms by the largest denominator present.

• Add the fractions together before solving the equation.

• Convert all fractions to decimals for easier calculation.

What happens if you multiply only some terms by the LCD?

• The equation will be equivalent, leading to correct solutions.

• The equation will not be equivalent, leading to incorrect solutions.

• The equation will simplify but remain unchanged.

• The equation will become more complex and difficult to solve.

What is the purpose of clearing fractions in an equation?

• To simplify the equation, making it easier to solve.

• To make the equation more complex and difficult to understand.

• To eliminate variables from the equation entirely.

• To change the equation into a different form without solving it.

When is it appropriate to use the GCF instead of the LCD?

• When simplifying fractions before solving an equation, but not for clearing fractions.

• When adding fractions with different denominators.

• When multiplying fractions to find a common denominator.

• When solving for a variable in a linear equation.

What do you do after finding the LCD?

• Add the LCD to every term of the equation.

• Multiply the LCD to every term of the equation.

• Divide every term of the equation by the LCD.

• Subtract the LCD from every term of the equation.

Solve: 8 = n + 3n - 24

• n = 5

• n = 8

• n = 10

• n = 12

What is a common mistake when solving equations with fractions?

• Forgetting to multiply every term by the least common denominator.

• Ignoring the fractions altogether and solving as if they were whole numbers.

• Only multiplying the first term by the least common denominator.

• Adding the least common denominator to each term instead of multiplying.

What does it mean to isolate a variable in an equation?

• To manipulate the equation so that the variable is on one side and all other terms are on the opposite side.

• To eliminate the variable from the equation entirely.

• To combine like terms on both sides of the equation.

• To substitute the variable with a constant value.