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7.5: Distributive Property and Solving for Unknowns Extras

Difficulty Level: At Grade Created by: CK-12
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Extra for Experts Distributive Property and Solving for Unknowns - Apply the Distributive Property

Figure out the value of each variable.

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\begin{align*}1. \quad 6 \div 2 \div 3 \times (f + 2) = 11\!\\ \!\\ {\;} \quad \ f = \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\!\\ \!\\ 2. \quad 37 = 3(m + 6) + 4(9-5)\!\\ \!\\ {\;} \quad \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;} = m\!\\ \!\\ 3. \quad (8 + 2) \div 5 \times (g + 4) = 32\!\\ \!\\ {\;} \quad \ g = \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\!\\ \!\\ 4. \quad 70 = 5 \times (9+ t) + 4 \times (t + 4)\!\\ \!\\ {\;} \quad \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;} = t\end{align*}1.6÷2÷3×(f+2)=11 f=2.37=3(m+6)+4(95) =m3.(8+2)÷5×(g+4)=32 g=4.70=5×(9+t)+4×(t+4) =t

Solutions

\begin{align*}1. \quad 6 \div 2 \div 3 \times (f + 2) = 11\!\\ {\;} \quad \ 1 \times (f + 2) = 11\!\\ {\;} \quad \ f + 2 = 11\!\\ {\;} \quad \ f = 9\end{align*}1.6÷2÷3×(f+2)=11 1×(f+2)=11 f+2=11 f=9

\begin{align*}2. \quad 37 = 3(m + 6) + 4(9-5)\!\\ {\;} \quad \ 37 = 3m + 18 + 4(9 - 5)\!\\ {\;} \quad \ 37 = 3m + 18 + 4 \times 4\!\\ {\;} \quad \ 37 = 3m + 18 + 16\!\\ {\;} \quad \ 37 = 3m + 34\!\\ {\;} \quad \ 3 = 3m\!\\ {\;} \quad \ 1 = m\end{align*}2.37=3(m+6)+4(95) 37=3m+18+4(95) 37=3m+18+4×4 37=3m+18+16 37=3m+34 3=3m 1=m

\begin{align*}3. \quad (8 + 2) \div 5 \times (g + 4) = 32\!\\ {\;} \quad \ 10 \div 5 \times (g + 4) = 32\!\\ {\;} \quad \ 2 \times (g + 4) = 32\!\\ {\;} \quad \ 2g + 8 = 32\!\\ {\;} \quad \ 2g = 24\!\\ {\;} \quad \ g = 12\end{align*}3.(8+2)÷5×(g+4)=32 10÷5×(g+4)=32 2×(g+4)=32 2g+8=32 2g=24 g=12

\begin{align*}4. \quad 70 = 5 \times (9 + t) + 4 \times (t + 4)\!\\ {\;} \quad \ 70 = 5 \times 9 + 5t + 4t + 4 \times 4\!\\ {\;} \quad \ 70 = 45 + 5t + 4t + 16\!\\ {\;} \quad \ 70 = 9t + 61\!\\ {\;} \quad \ 9 = 9t\!\\ {\;} \quad \ 1 = t\end{align*}4.70=5×(9+t)+4×(t+4) 70=5×9+5t+4t+4×4 70=45+5t+4t+16 70=9t+61 9=9t 1=t

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CK.MAT.ENG.SE.1.Algebra-Explorations-K-7.7.5