FIND T

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[tex]\begin{gathered}{\underline{\huge \mathbb{A} {\large \mathbf {NSWER : }}}} \\\end{gathered}[/tex]

[tex]\begin{gathered} \qquad \qquad \quad\qquad \large \bm{t=-4} \\ \end{gathered}[/tex]

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[tex]\begin{gathered}{\underline{\huge \mathbb{S} {\large \mathbf {OLUTION : }}}} \\\end{gathered} [/tex]

• To find t given the equation, simplify the left side.

Given:

[tex]\begin{gathered}\qquad\qquad\sf\hookrightarrow \: \boxed{\bold{ \: \: \: 3(2t-1) = 7t+1 \: \: \: }} \\ \end{gathered}[/tex]

So,

[tex]\begin{gathered} \qquad \quad\sf\implies \: 3(2t)+3(-1) = 7t + 1 \\ \end{gathered}[/tex]

[tex]\begin{gathered} \qquad \quad\sf\implies \: 6t+(-3) = \bold{7t+1} \\ \end{gathered}[/tex]

[tex]\begin{gathered} \qquad \quad\sf\implies \: 6t+-3 = \bold{7t+1} \\ \end{gathered}[/tex]

[tex]\qquad \qquad{ \overline{ \qquad \qquad \qquad \qquad \qquad}} [/tex]

• Add 3 to each side:

[tex]\begin{gathered} \qquad \quad\sf\implies 6t -3+3 = \bold{7t+1+3} \\ \end{gathered} [/tex]

[tex]\begin{gathered} \qquad \quad\sf\implies \: 6t = \bold{7t+4} \\ \end{gathered} [/tex]

[tex]\qquad \qquad{ \overline{ \qquad \qquad \qquad \qquad \qquad}} [/tex]

• Subtract 7t from both sides:

[tex]\begin{gathered} \qquad \quad\sf\implies \: 6t-7t= 7t +7t+4 = \\ \bold{-t=-4} \\ \end{gathered} [/tex]

• Divide both sides by -1

[tex]\begin{gathered} \qquad \quad\sf\implies \: \dfrac{ - t}{ - 1} = \bold{ \dfrac{ 4}{ - 1} } \\ \end{gathered} [/tex]

[tex]\begin{gathered} \\ \end{gathered} [/tex]

[tex]\begin{gathered} \qquad \qquad \qquad \: \sf{t = \bold{ -4}} \\ \end{gathered} [/tex]

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