how do you solve this
can you please show me step by step
y/2 -5y/6 +1/3= 1/2
15/8z + 1/4 = 4
Isolate the unknown on one side by subtracting 1/4 from both sides.
15/8z = 15/4 = 30/8
Divide both sides by 15/8 = multiply by 8/15
z = 2
Now you try the first equation.
To solve the equation y/2 - 5y/6 + 1/3 = 1/2, you can follow these step-by-step instructions:
Step 1: Clear the fractions by multiplying every term in the equation by the least common denominator (LCD) of all the denominators. In this case, the LCD is 6.
Multiply each term by 6:
6*(y/2) - 6*(5y/6) + 6*(1/3) = 6*(1/2)
3y - 5y + 2 = 3
Simplify all the terms:
3y - (5y/6) + 2/3 = 3
Step 2: Combine like terms. In this case, you have two terms with y:
Multiply the denominator of the second term by the numerator of the first term to get a common denominator. Then combine the terms:
(18y - 5y)/6 + 2/3 = 3
(13y/6) + 2/3 = 3
Step 3: Isolate the variable term. To do this, subtract 2/3 from both sides of the equation:
(13y/6) = 3 - 2/3
(13y/6) = 7/3
Step 4: To get rid of the fraction coefficient, multiply both sides of the equation by the reciprocal of the fraction. In this case, multiply both sides by 6/13:
(6/13) * (13y/6) = (6/13) * (7/3)
y = 42/39
Simplify the fraction if possible:
y = 14/13
Therefore, the solution to the equation y/2 - 5y/6 + 1/3 = 1/2 is y = 14/13.
Now, let's proceed to solve the equation 15/8z + 1/4 = 4:
Step 1: Clear the fractions by multiplying every term in the equation by the least common denominator (LCD) of all the denominators. In this case, the LCD is 8.
Multiply each term by 8:
8 * (15/8z) + 8 * (1/4) = 8 * 4
15z + 2 = 32
Step 2: Isolate the variable term. To do this, subtract 2 from both sides of the equation:
15z + 2 - 2 = 32 - 2
15z = 30
Step 3: Solve for z by dividing both sides by 15:
15z/15 = 30/15
z = 2
Therefore, the solution to the equation 15/8z + 1/4 = 4 is z = 2.