Question

Solve for t: 15 = -6t - (3/5) x (3 - 2t).

I know you can multiply both sides by 5 to get rid of the fraction, but do I need to multiply (3 - 2t) by 5 or not?

Please help thank you (just respond yes or no)!

Answer 1

`\pink{t = - 3.5}`

Explanation:

`\text{solve \: the \: brackets} \\ 15 = - 6t - (3)/(5) (3 - 2t) \\15 = - 6t - (9)/(5) + (6t)/(5) \\ \text{combine \: like \: terms } \\ 15 = ( - 6t * 5)/(1 * 5) - (9)/(5) + (6t)/(5) \\ 15 = ( - 30t)/(5) - (9)/(5) + (6t)/(5) \\15 = ( - 24t)/(5) - (9)/(5) \\ 15 = ( - 24t - 9)/(5) \\ \text{use \: cross \: multiplication} \\ 15 * 5 = - 24t - 9 \\ 75 = - 24t - 9 \\ 75 + 9 = - 24t \\ 84 = - 24t \\ \text{ \: divide \: both \: sides \: by \: } - 24 \\ - 3.5 = t`

Answer 2

-7/2 = t

Explanation:

15 = -6t - (3/5) * (3 - 2t)

Solve for t

Multiply each side by 5 to clear the fractions

5 * 15 = 5*-6t - 5* (3/5) * (3 - 2t)

The 5 cancels the 5 in the denominator of the fraction 3/5 leaving only the 3.

75 = -30t - 3 ( 3-2t)

Distribute

75 = -30t -9 + 6t

Combine like terms

75 = -24t -9

Add 9 to each side.

75 +9 = -24t-9+9

84 = -24t

Divide each side by -24

84/-24 = -24t/-24

-7/2 = t