Solve the equation or inequality for
3(2y-4)=9-3(y+1)The answer is 2. How do you work it out to get the answer?
(x+5)(x-3)=9 the answer is -6,4
How do you work it out????
first one:
3(2y-4)=9-3(y+1)
6y - 12 = 9 - 3y - 3
6y + 3y = 6+12
9y = 18
y = 2
2nd:
(x+5)(x-3)=9
x^2 - 3x + 5x - 15 = 9
x^2 + 2x - 24 = 0
(x+6)(x-4) = 0
so x+6 = 0 or x-4 = 0
x = -6 or x = 4
To solve the equation 3(2y-4) = 9-3(y+1) for y and find the solution 2, you can follow these steps:
1. Distribute the 3 on the left side and the -3 on the right side of the equation:
6y - 12 = 9 - 3y - 3
2. Combine like terms on both sides:
6y + 3y = 9 + 3 - (-12)
9y = 24
3. Divide both sides of the equation by 9 to isolate the variable y:
y = 24/9
4. Simplify the right side of the equation:
y = 8/3
5. Convert the fraction to a decimal or mixed number:
y ≈ 2.67
So the solution to the equation is y ≈ 2.67, which is approximately 2.
To solve the equation (x+5)(x-3) = 9 and find the solutions -6 and 4, you can use the following steps:
1. Expand the left side of the equation using the distributive property:
x^2 - 3x + 5x - 15 = 9
2. Combine like terms on the left side:
x^2 + 2x - 15 = 9
3. Move the constant term to the right side by subtracting 9 from both sides:
x^2 + 2x - 15 - 9 = 9 - 9
x^2 + 2x - 24 = 0
4. Factor the quadratic expression:
(x - 3)(x + 8) = 0
5. Set each factor equal to zero and solve for x:
x - 3 = 0 or x + 8 = 0
x = 3 or x = -8
So the solutions to the equation are x = 3 and x = -8, which corresponds to the answer -6 and 4 when plugged back into the original equation.