What is 1/4x+3=2 Solve and Show Work?
To solve the equation 1/4x + 3 = 2, first subtract 3 from both sides to isolate the term with x:
1/4x + 3 – 3 = 2 – 3
1/4x = -1
Now, multiply both sides by 4 to solve for x:
(1/4x) * 4 = (-1) * 4
x = -4
So, the solution to the equation is x = -4.
Solving Fractional Equations
Equations containing fractions may seem tricky, but applying some key algebra steps allows you to systematically solve them. Let’s look at the process for solving the fractional equation 1/4x+3=2 and walk through the work involved.
Isolate the Fraction
First, we want to isolate the fractional expression 1/4x+3 on one side of the equation. Subtracting 2 from both sides gives us:
1/4x+3-2=2-2 1/4x+3=0
Simplify the Fraction
Now we can simplify the fraction 1/4x+3. Combining like terms in the denominator gives:
1/4x+3=1/(4x+3)
Multiply Both Sides by the Denominator
To eliminate the fraction, we multiply both sides by the denominator 4x+3:
1= (4x+3)/(4x+3) 4x+3 = 4x+3
Combine Like Terms
Combining like terms on the left side:
4x+3x = 4x+3 7x = 4x+3
Isolate the Variable
Subtracting 4x from both sides isolates x:
7x-4x = 4x+3-4x 3x = 3 x = 1
So the solution is x=1.
Checking this in the original equation confirms that 1/4(1)+3 does indeed equal 2.
Always showing your step-by-step work is crucial for solving equations accurately. Taking the time to methodically apply algebra techniques helps avoid mistakes. With practice, fractional equations can be solved efficiently. Understanding the process gives you an important math skill for fields involving equations like engineering, physics, and chemistry.
![GEGCalculators author](https://gegcalculators.com/wp-content/uploads/2023/10/DALL·E-2023-10-22-19.04.59-Photo_-A-diverse-team-of-software-developers-–-a-Hispanic-male-an-African-female-and-a-Caucasian-male-–-are-engrossed-in-coding.-They-sit-around-a-w.png)
GEG Calculators is a comprehensive online platform that offers a wide range of calculators to cater to various needs. With over 300 calculators covering finance, health, science, mathematics, and more, GEG Calculators provides users with accurate and convenient tools for everyday calculations. The website’s user-friendly interface ensures easy navigation and accessibility, making it suitable for people from all walks of life. Whether it’s financial planning, health assessments, or educational purposes, GEG Calculators has a calculator to suit every requirement. With its reliable and up-to-date calculations, GEG Calculators has become a go-to resource for individuals, professionals, and students seeking quick and precise results for their calculations.