Which value of x is the solution of the equation
1/7 + 2x/3 = (15x-3)/(21) ?
(Those are fractions)
(1) 6
(2) 0
(3) 4/13
(4) 6/29
way 1: try each answer and get (1)
way 2: solve algebraically
1/7 + 2x/3 = (15x-3)/(21)
3 + 14x = 15x-3
x = 6
Thanks! I just did, makes sense!
To find the value of x that is the solution of the equation 1/7 + 2x/3 = (15x-3)/(21), follow these steps:
Step 1: Clear the denominators by multiplying every term in the equation by the least common denominator (LCD), which in this case is 21:
21 * (1/7) + 21 * (2x/3) = 21 * ((15x-3)/(21))
Step 2: Simplify the equation:
3 + 14x = 15x - 3
Step 3: Isolate the variable terms on one side of the equation. Subtract 15x from both sides and add 3 to both sides:
3 - 15x + 14x = 15x - 3 - 15x + 3
3 - x = 0
Step 4: Solve for x by moving the x term to the other side of the equation. Subtract 3 from both sides:
3 - x - 3 = 0 - 3
-x = -3
Step 5: Flip the sign on both sides of the equation to solve for x:
x = 3
Therefore, the value of x that is the solution of the equation is (2) 0.
To find the value of x that is a solution to the equation, we need to simplify and solve the equation step by step. Here's how you can do it:
Step 1: Clear the fractions by multiplying both sides of the equation by a common denominator. In this case, the common denominator is 21.
(21) * (1/7) + (21) * (2x/3) = (21) * ((15x-3)/21)
After multiplying, the equation becomes:
3 + 14x = 15x - 3
Step 2: Simplify the equation by combining like terms. In this case, we have the variable term (14x and 15x) on the right side and the constant term (3 and -3) on the left side.
Subtract 14x from both sides of the equation:
3 = x - 3
Now, we have:
3 + 3 = x
6 = x
Step 3: Check if the solution satisfies the equation. Substitute x = 6 back into the original equation:
1/7 + 2(6)/3 = (15(6)-3)/21
1/7 + 12/3 = (90-3)/21
1/7 + 4 = 87/21
1/7 + 28/7 = 87/21
29/7 = 87/21
The left side equals 29/7, while the right side equals 87/21. These two values are equivalent since they reduce to the same fraction.
Step 4: Identify the value of x that satisfies the equation. Since x = 6 satisfies the equation, the correct answer is option (1) 6.
Therefore, the value of x that is the solution to the equation is 6.