Question

Enter the value of n so the expression (-y+ 5.3) + (7.2y-9) is equivalent to 6.2y+n.

Answer 1

`\boxed{\bold{Decimal: \ n \ = \ -3.7}}`

`\boxed{\bold{Fraction: \ n=-(37)/(10)}}`

Step By Step Explanation:

Rewrite Equation:

`\bold{\left(-y+5.3\right)+\left(7.2y-9\right)=6.2y+n}`

Switch Sides:

`\bold{6.2y+n=\left(-y+5.3\right)+7.2y-9}`

Remove Parenthesis: (a) = a

`\bold{6.2y+n=-y+5.3+7.2y-9}`

Group Like Terms:

`\bold{6.2y+n=-y+7.2y+5.3-9}`

Combine Similar Elements:
`\bold{-y+7.2y=6.2y}`

`\bold{6.2y+n=6.2y+5.3-9}`

Subtract:
`\bold{5.3-9=-3.7}`

`\bold{6.2y+n=6.2y-3.7}`

Multiply Both Sides By 10:

`\bold{6.2y\cdot \:10+n\cdot \:10=6.2y\cdot \:10-3.7\cdot \:10}`

Refine:

`\bold{62y+10n=62y-37}`

Subtract 62y From Both Sides:

`\bold{62y+10n-62y=62y-37-62y}`

Refine:

`\bold{10n=-37}`

Divide Both Sides By 10:

`\bold{(10n)/(10)=(-37)/(10)}`

Simplify:

`\bold{n=-(37)/(10)}`

Turn Fraction Into Decimal:

`\bold{-37 \ / \ 10}`

Refine:

`\bold{-3.7}`

- Mordancy