PROBLEM:
A government official's budget is represented by [tex] \tt6x² + 13x + 2[/tex]. Find the amount of budget after [tex] \tt3x + 29[/tex] was used for the construction of the library.
SOLUTION:
To find the amount budget after some amount was used, we need to subtract the amount used for the construction of the library from the government official's budget.
• We'll have the algebraic expression: [tex] \tt6x² + 13x + 2 - ( \tt3x + 29)[/tex].
- [tex]\tt - (3x + 29) = - 3x - 29[/tex]
[tex] \huge \purple{ \overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
[tex]\huge{\boxed{\large\begin{array}{l} \tt \: \: \: \tt6x² + 13x + 2 \\ \tt \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: - \: 3x - 29 \: \: \: } \\ \tt \: \: \: 6x {}^{2} + 10x - 27 \end{array}}}[/tex]
[tex] \huge \purple{ \overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
ANSWER:
The amount of budget after [tex]\tt 3x + 29 [/tex] was used for the construction of the library is [tex] \tt\purple{ 6x {}^{2} + 10x - 27} [/tex].
