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Solve the following equation algebraically. Show your work.
6=x+2/3
To solve the equation algebraically, we need to isolate the variable x.
First, let's get rid of the fraction by multiplying both sides of the equation by the denominator, which is 3:
3 * 6 = 3 * (x + 2/3)
18 = 3x + 2
Next, let's isolate the term with x by subtracting 2 from both sides of the equation:
18 - 2 = 3x + 2 - 2
16 = 3x
To find the value of x, we need to divide both sides of the equation by 3:
16/3 = 3x/3
Simplifying the right side:
16/3 = x
Therefore, the value of x is 16/3.
To solve the equation algebraically, we need to isolate the variable x on one side of the equation.
Step 1: Start with the equation: 6 = x + 2/3.
Step 2: To eliminate the fraction, we can multiply both sides of the equation by the reciprocal of the fraction, which is 3/2. This will cancel out the fraction on the right side of the equation.
6 × (3/2) = (x + 2/3) × (3/2)
Step 3: Simplify both sides of the equation:
(6 × 3)/2 = (3x + 2/3) × (3/2)
18/2 = (3x × 3/2) + (2/3 × 3/2)
9 = (9x/2) + (4/6)
Step 4: Simplify further by finding a common denominator:
9 = (9x + 4)/6
Step 5: To get rid of the fraction, we can cross-multiply:
6 × 9 = 9x + 4
Step 6: Simplify:
54 = 9x + 4
Step 7: To isolate x, subtract 4 from both sides of the equation:
54 - 4 = 9x + 4 - 4
50 = 9x
Step 8: Finally, divide both sides of the equation by 9 to solve for x:
50/9 = (9x)/9
x = 50/9
Therefore, the solution to the equation 6 = x + 2/3 is x = 50/9.
To solve the equation 6 = x + 2/3 algebraically, we need to isolate x on one side of the equation. Here are the steps:
Step 1: Subtract 2/3 from both sides to get rid of the addition on the right side of the equation:
6 - 2/3 = x + 2/3 - 2/3
Simplifying the left side of the equation:
6 - 2/3 = 18/3 - 2/3
18/3 is the same as 6, so we have:
6 - 2/3 = 6 - 2/3
Step 2: Simplify both sides of the equation:
6 - 2/3 = 6 - 2/3
4 + 4/3 or 12/3 + 2/3 = x
Step 3: Combine like terms:
4 + 4/3 = 12/3 + 2/3
4/1 + 4/3 = 12/3 + 2/3
12/3 can be simplified to 4/1, so we have:
4/1 + 4/3 = 4/1 + 2/3
Step 4: Convert both fractions to have a common denominator, which is 3:
4/1 + 4/3 = 4/1 + 2/3
12/3 + 4/3 = 12/3 + 2/3
16/3 = 14/3
Therefore, the simplified equation is:
16/3 = 14/3
Step 5: Since the left side is not equal to the right side of the equation, there is no solution to this equation.
Therefore, there is no value of x that will satisfy the equation 6 = x + 2/3.