Question

1) -5(4,2y+1)+4(1,4y-2)=-20,2 2) - 5/7-(m-1)=11/14 3) 1 5/6-(y+2/3)=1 1/2

Answer 1

1)-21y-5+5.6y-8=-20.2
-15.4y-13=-20.2
-15.4y=-20.2+13
-15.4y=-7.2
y=36/77
2)-5/7-m+1=11/14
-m+2/7=11/14
-m=11/14-2/7
-m=0.5
m=-0.5
3)1 5/6-y-2/3=1 1/2
-y+1 1/6=1 1/2
-y=1 1/2- 1 1/6
-y=-1/3
y=1/3

Answer 2

To solve these equations, we'll follow the standard algebraic steps to isolate the variable on one side of the equation. Let's solve each equation step-by-step:

1. -5(4, 2y+1) + 4(1, 4y-2) = -20, 2

It seems like you're dealing with vectors or coordinates in this equation. However, it's not clear what the variables represent. Assuming that (4, 2y + 1) and (1, 4y - 2) are points in a coordinate system, we'll try to solve the equation:

-5(4, 2y+1) + 4(1, 4y-2) = (-20, 2)

To perform the operations, we distribute the scalar values:

(-20, -10y - 5) + (4, 16y - 8) = (-20, 2)

Now, combine the corresponding components:

-20 + 4 = -20 => This is true for the x-component. -10y - 5 + 16y - 8 = 2 => Combine the y-components. 6y - 13 = 2 6y = 2 + 13 6y = 15 y = 15/6 y = 2.5

So, the solution is y = 2.5.

2. -5/7 - (m - 1) = 11/14

To solve for m, first, let's isolate the term containing m:

-5/7 - m + 1 = 11/14

Now, combine constants:

1 - 5/7 = 11/14 + m

To combine the fractions, find a common denominator:

(14 - 10)/14 = 11/14 + m

Now, continue solving:

4/14 = 11/14 + m

To isolate m, subtract 11/14 from both sides:

4/14 - 11/14 = m

-7/14 = m

Simplify the fraction:

m = -1/2

So, the solution is m = -1/2.

3. 1 5/6 - (y + 2/3) = 1 1/2

To solve for y, first, let's convert the mixed numbers into improper fractions:

1 5/6 = (61 + 5)/6 = 11/6 1 1/2 = (21 + 1)/2 = 3/2

Now, rewrite the equation:

11/6 - (y + 2/3) = 3/2

To isolate y, first, distribute the negative sign:

11/6 - y - 2/3 = 3/2

Next, combine the constants:

11/6 - 2/3 = y + 3/2

To combine the fractions, find a common denominator:

(22 - 4)/6 = y + 3/2

Now, continue solving:

18/6 = y + 3/2

To simplify, divide both sides by 3:

3 = y + 3/2

To isolate y, subtract 3/2 from both sides:

3 - 3/2 = y

(6 - 3)/2 = y

3/2 = y

So, the solution is y = 3/2.