Question

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

Answer 1

Answer:

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

$\boxed{\bold{Fraction: \ n=-\frac{37}{10}}}$

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:

$\bold{\frac{10n}{10}=\frac{-37}{10}}$

Simplify:

$\bold{n=-\frac{37}{10}}$

Turn Fraction Into Decimal:

$\bold{-37 \ \div \ 10}$

Refine:

$\bold{-3.7}$

- Mordancy