Solving Equations with Fraction Coefficients

Front

What is the process for solving an equation with a fraction coefficient?

Back

To solve an equation with a fraction coefficient, first eliminate the fractions by multiplying every term by the least common denominator (LCD). Then, simplify and isolate the variable.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to both sides of the equation until the variable is alone on one side. This may involve adding, subtracting, multiplying, or dividing.

Front

What is the least common denominator (LCD) and why is it important?

Back

The least common denominator (LCD) is the smallest multiple that two or more denominators share. It is important because it allows you to eliminate fractions in equations, making them easier to solve.

Front

What does it mean to solve an inequality?

Back

Solving an inequality involves finding the range of values for the variable that makes the inequality true, often resulting in a solution expressed as an interval or a set of values.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than, less than, or not equal to another.

Front

How do you check your solution to an equation?

Back

To check your solution, substitute the value back into the original equation to see if both sides are equal.

Front

What is a coefficient in an algebraic expression?

Back

A coefficient is a numerical factor that multiplies a variable in an algebraic expression.

Front

What is the first step in solving the equation \( \frac{3}{4}x + \frac{2}{3} = \frac{1}{2}x - \frac{1}{6} \)?

Back

The first step is to eliminate the fractions by multiplying every term by the least common denominator, which in this case is 12.

Front

What is the solution to the equation \( \frac{1}{2}x + \frac{1}{4} = \frac{3}{4}x - \frac{1}{2} \)?

Back

The solution is x = 3.

Front

How do you solve the inequality \( \frac{5}{9}x - \frac{1}{3} < \frac{4}{9}x + \frac{2}{9} \)?

Back

First, isolate x by moving all terms involving x to one side and constant terms to the other side, then solve for x.