Question

Solve for x using common denominators. 3 over the quantity 4 times the binomial x plus 2 equals x over the quantity x plus 2 −4 over 3 4 over 3 −3 over 4 3 over 4

Answer 1

To solve for x with a common denominator, you should express all terms using the same denominator, combine them, and then solve for x. In the process, you may need to multiply both sides by the least common denominator or cross multiply in proportions.

Step-by-step explanation:

To solve an equation with a common denominator, you want to first make sure each term is expressed with the same denominator. This allows you to combine the terms and then solve for the variable, in this case, x.

Let's look at an example that uses a similar process:

First, set up a proportion like 1 gallon/4 quarts = 3 gallons/x quarts. To solve for x, you cross multiply to get 1x = 3×4. Simplify the equation by performing the multiplication to find out that x equals 12 quarts.

Another example involves simplifying fractions: (2x)² = 4.0 (1 − x)². You can take the square root of both sides and solve for x by rearranging the result.

When multiplying fractions, such as 1/4-3/x, simply multiply the numerators together and multiply the denominators together, and then simplify as needed.

For equations where terms are fractions, it's often helpful to multiply both sides by the least common denominator to eliminate the fractions altogether and make the equation easier to solve.