Question

-3(u+2)=5u-1+5(2u+1)

Answer 1

`\sf u = -(5)/(9)`

Explanation:

Expand the following:

`\longrightarrow` -3(u + 2) = 5u - 1 + 5(2u + 1)

5(2u + 1) = 10u + 5:

`\longrightarrow` -3(u + 2) = 5u - 1 + 10u + 5

-3(u + 2) = -3u - 6:

`\longrightarrow` -3u - 6= 10 u + 5 u - 1 + 5

Grouping like terms,

5u - 1 + 10u + 5 = (5u + 10u) + (-1 + 5):

`\longrightarrow` -3u - 6 = (5u + 10u) + (-1 + 5)

5u + 10u = 15u:

`\longrightarrow` -3u - 6 = 15u + (-1 + 5)

5 - 1 = 4:

`\longrightarrow` -3u - 6 = 15u + 4

Subtract 15 u from both sides:

`\longrightarrow` (-3u - 15u) - 6 = (15u - 15u) + 4

-3u - 15u = -18u:

`\longrightarrow` -18u - 6 = (15u - 15u) + 4

15u - 15u = 0:

`\longrightarrow` -18u - 6 = 4

Add 6 to both sides:

`\longrightarrow` (6 - 6) - 18u = 6 + 4

6 - 6 = 0:

`\longrightarrow` -18u = 4 + 6

4 + 6 = 10:

`\longrightarrow` -18u = 10

Divide both sides of -18 u = 10 by -18:

`\longrightarrow`
`\sf (-18u)/(-18)= (10)/(-18)`

`\sf (-18)/(-18)=1:`

`\longrightarrow`
`\sf u = (10)/(-18)`

`\sf (10)/(-18)=(5)/(-9):`

`\longrightarrow`
`\sf u = (5)/(-9)`

Multiply numerator and denominator of
`\sf (10)/(-18)` by -1:

`\longrightarrow`
`\sf u = (-5)/(9)`

Answer 2

u = -5/9

General Formulas and Concepts:

Pre-Algebra

• Order of Operations: BPEMDAS
• Equality Properties

Explanation:

Step 1: Define equation

-3(u + 2) = 5u - 1 + 5(2u + 1)

Step 2: Solve for u

1. Distribute: -3u - 6 = 5u - 1 + 10u + 5
2. Combine like terms: -3u - 6 = 15u + 4
3. Add 3u to both sides: -6 = 18u + 4
4. Subtract 4 on both sides: -10 = 18u
5. Divide 18 on both sides: -10/18 = u
6. Simplify: -5/9 = u
7. Rewrite: u = -5/9

Step 3: Check

Plug in u into the original equation to verify it's a solution.

1. Substitute in u: -3(-5/9 + 2) = 5(-5/9) - 1 + 5(2(-5/9) + 1)
2. Multiply: -3(-5/9 + 2) = -25/9 - 1 + 5(-10/9 + 1)
3. Add: -3(13/9) = -25/9 - 1 + 5(-1/9)
4. Multiply: -13/3 = -25/9 - 1 - 5/9
5. Subtract: -13/3 = -34/9 - 5/9
6. Subtract: -13/3 = -13/3

Here we see that -13/3 does indeed equal -13/3.

∴ u = -5/9 is a solution of the equation.