how do you solve these
please show me how you do these step by step
1. y/2 -5y/6 +1/3= 1/2
2. 15/8z + 1/4 = 4
3. 4/5 - 2p/5= 6/5
thank you
First, get the unknown alone on one side.
3. 2p/5 = 2/5p
2/5p = 2/5
Can you work it and the others from there?
To solve these equations step by step, we will use the concept of isolating the variable, which means we want to get the variable alone on one side of the equation.
Let's solve each equation one by one:
1. y/2 - 5y/6 + 1/3 = 1/2
To combine the fractions, we need to find a common denominator. In this case, the least common multiple of 2, 6, and 3 is 6. So we multiply the first term by 3/3, the second term by 2/2, and the third term by 2/2 to obtain a common denominator of 6.
(3y/6) - (5y/6) + (2/6) = 1/2
Now we can combine the fractions:
(3y - 5y + 2) / 6 = 1/2
Combine like terms:
(-2y + 2) / 6 = 1/2
To isolate the variable, we'll multiply both sides of the equation by the common denominator, which is 6:
6 * (-2y + 2) / 6 = (1/2) * 6
Simplify:
-2y + 2 = 3
Next, let's move the constant term to the other side by subtracting 2 from both sides:
-2y = 3 - 2
Simplify:
-2y = 1
Lastly, divide both sides by -2 to solve for y:
-2y / -2 = 1 / -2
y = -1/2
Therefore, the solution to the equation is y = -1/2.
2. 15/8z + 1/4 = 4
To combine the fractions, we need to find a common denominator. In this case, the least common multiple of 8 and 4 is 8. So we multiply the first term by 1/1 and the second term by 2/2 to obtain a common denominator of 8.
(15/8z) + (2/8) = 4
Now, let's combine the fractions:
(15 + 2) / 8z = 4
Simplify:
17/8z = 4
To isolate the variable, we'll multiply both sides of the equation by 8:
8 * (17/8z) = 4 * 8
Simplify:
17/z = 32
Next, we'll move the constant term to the other side by dividing both sides by 32:
17/z = 32/1
Simplify:
17/z = 32
Now, we can cross-multiply:
17 = 32z
To solve for z, divide both sides by 32:
17/32 = z
Therefore, the solution to the equation is z = 17/32.
3. 4/5 - 2p/5 = 6/5
To combine the fractions, we need to have a common denominator. In this case, the denominator is already the same (5), so we don't need to do anything.
Now, let's combine the fractions:
(4 - 2p)/5 = 6/5
Since the denominators are the same, we can equate the numerators:
4 - 2p = 6
To isolate the variable, let's subtract 4 from both sides:
4 - 2p - 4 = 6 - 4
Simplify:
-2p = 2
Divide both sides by -2:
(-2p)/-2 = 2/-2
Simplify:
p = -1
Therefore, the solution to the equation is p = -1.