Studdy AI Logo
Math  /  Algebra

Questionthe equation 2x+13−x4=2\frac{2 x+1}{3}-\frac{x}{4}=2

Studdy Solution

STEP 1

1. The equation 2x+13−x4=2\frac{2x+1}{3} - \frac{x}{4} = 2 is a linear equation in one variable.
2. The goal is to solve for xx.
3. The equation involves fractions, so we will need to find a common denominator to simplify the equation.

STEP 2

1. Eliminate the fractions by finding a common denominator.
2. Simplify the equation to isolate the variable xx.
3. Solve for xx.
4. Check the solution by substituting it back into the original equation.

STEP 3

Identify the least common denominator (LCD) of the fractions. The denominators are 3 and 4, so the LCD is 12.
Multiply every term in the equation by 12 to eliminate the fractions:
12(2x+13)−12(x4)=12×2 12 \left(\frac{2x+1}{3}\right) - 12 \left(\frac{x}{4}\right) = 12 \times 2

STEP 4

Simplify each term:
4(2x+1)−3x=24 4(2x+1) - 3x = 24

STEP 5

Distribute the numbers in the equation:
8x+4−3x=24 8x + 4 - 3x = 24
Combine like terms:
5x+4=24 5x + 4 = 24

STEP 6

Isolate the variable xx by subtracting 4 from both sides:
5x=20 5x = 20
Divide both sides by 5:
x=4 x = 4

STEP 7

Check the solution by substituting x=4x = 4 back into the original equation:
2(4)+13−44=2 \frac{2(4)+1}{3} - \frac{4}{4} = 2
Simplify each term:
93−1=2 \frac{9}{3} - 1 = 2
3−1=2 3 - 1 = 2
Both sides are equal, confirming the solution is correct.
The solution is:
4 \boxed{4}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord