solve the equation and check
1/5(y+3)+3=1/10(7y-4)-5
1/5(y+3)+3=1/10(7y-4)-5
1/5y + 3/5 + 3 = 7/10y - 4/10 - 5
Take it from there.
I'll be glad to check your answer.
y= -4.7
Please check your figures.
I get 4.5
i did 7/10y- 4/10 y=.3-5 which equal -4.7
To solve the equation 1/5(y+3)+3=1/10(7y-4)-5 and check the solution, follow these steps:
Step 1: Distribute the fractions to simplify the equation.
Start by distributing 1/5 to the terms inside the parentheses (y+3) and distribute 1/10 to the terms inside the parentheses (7y-4).
(1/5) * (y+3) + 3 = (1/10) * (7y-4) - 5
This simplifies to:
(y/5) + (3/5) + 3 = (7y/10) - (4/10) - 5
Step 2: Combine like terms.
Combine the fractions with the same denominator and simplify the constants.
(y/5) + (3/5) + 3 = (7y/10) - (4/10) - 5
Simplify the constants:
(y/5) + (3/5) + 3 = (7y/10) - (4/10) - 5
(y/5) + 3 + 3 = (7y/10) - 4/10 - 5
(y/5) + 6 = (7y/10) - 9/10
Step 3: Get rid of the fractions by multiplying through by the least common denominator (LCD).
The LCD in this case is 10:
Multiply all terms by 10 to clear the fractions.
10 * [(y/5) + 6] = 10 * [(7y/10) - 9/10]
This simplifies to:
2y + 60 = 7y - 9
Step 4: Combine like terms.
Combine the terms with variables and the terms with constants on each side of the equation.
2y + 60 = 7y - 9
Add -7y on both sides:
2y - 7y + 60 = 7y - 7y - 9
This simplifies to:
-5y + 60 = -9
Step 5: Solve for y.
Isolate the variable y by moving the constants to the other side of the equation.
Start by subtracting 60 from both sides.
-5y + 60 - 60 = -9 - 60
This simplifies to:
-5y = -69
Next, divide both sides by -5 to solve for y.
-5y / -5 = -69 / -5
This simplifies to:
y = 13.8
Step 6: Check the solution.
To check if y = 13.8 is the correct solution, substitute the value into the original equation and see if both sides are equal.
1/5(y+3)+3=1/10(7y-4)-5
Substitute y = 13.8:
1/5(13.8+3)+3=1/10(7*13.8-4)-5
Simplify:
(1/5 * 16.8) + 3 = (1/10 * 95.6 - 4) - 5
(3.36) + 3 = (9.56 - 4) - 5
6.36 = 5.56 - 5
6.36 = 0.56
Since the left side does not equal the right side, the solution y = 13.8 does not check out. Therefore, there is no solution to the equation.