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\( \begin{array}{lll}\begin{array}{lll}\text { (a) } 3 g=6.3\end{array} \\ \begin{array}{ll}\text { (b) } 5 x=12+18\end{array} \\ & \text { (c) } 2(a+2 a)=90\end{array} \)

Ask by Wright Peters. in Germany
Mar 09,2025

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Tutor-Verified Answer

Answer

**(a)** \( g = 2.1 \) **(b)** \( x = 6 \) **(c)** \( a = 15 \)

Solution

**(a)** We start with the equation \[ 3g = 6.3 \] To solve for \(g\), divide both sides by 3: \[ g = \frac{6.3}{3} = 2.1 \] --- **(b)** The equation is \[ 5x = 12 + 18 \] First, compute the sum on the right-hand side: \[ 12 + 18 = 30 \] Now the equation becomes: \[ 5x = 30 \] Divide both sides by 5 to solve for \(x\): \[ x = \frac{30}{5} = 6 \] --- **(c)** The equation is \[ 2(a + 2a) = 90 \] Combine like terms inside the parentheses: \[ a + 2a = 3a \] Thus, the equation becomes: \[ 2(3a) = 90 \quad \Longrightarrow \quad 6a = 90 \] Divide both sides by 6 to solve for \(a\): \[ a = \frac{90}{6} = 15 \]

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In the realm of algebra, this set of equations showcases the beauty of solving for unknowns. We're essentially peeling back the layers of a mathematical mystery! For (a), we can divide both sides by 3 to find \( g = 2.1 \). In (b), add up the right side to simplify: \( 5x = 30 \) thus \( x = 6 \). For (c), simplify \( 2(a + 2a) = 90 \) which leads to \( 2(3a) = 90 \); then divide by 6 to find \( a = 15 \). Understanding foundational concepts like balancing equations helps illuminate the path to finding solutions. Remember, every variable you isolate is like unlocking a treasure chest full of valuable insights that could lead you to more complex mathematical conquests in the future!

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