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Solve the equation

5(2x+3)+3(5x-2)=84

1 answer

To solve the equation \(5(2x + 3) + 3(5x - 2) = 84\), let's start by distributing the terms on the left-hand side.

  1. Distribute the \(5\) into \(5(2x + 3)\): \[ 5 \cdot 2x + 5 \cdot 3 = 10x + 15 \]

  2. Distribute the \(3\) into \(3(5x - 2)\): \[ 3 \cdot 5x + 3 \cdot (-2) = 15x - 6 \]

  3. Now, combine these results: \[ 10x + 15 + 15x - 6 = 84 \]

  4. Combine like terms: \[ (10x + 15x) + (15 - 6) = 84 \] \[ 25x + 9 = 84 \]

  5. Next, isolate \(25x\) by subtracting \(9\) from both sides: \[ 25x = 84 - 9 \] \[ 25x = 75 \]

  6. Finally, divide both sides by \(25\) to solve for \(x\): \[ x = \frac{75}{25} \] \[ x = 3 \]

Thus, the solution to the equation is \( \boxed{3} \).