To solve the equation \( 5(x + 3) - 7(x - 4) = 38 \), follow these steps:
-
Distribute the \(5\) and \(-7\) to the terms inside the parentheses: \[ 5(x) + 5(3) - 7(x) + 7(4) = 38 \] This simplifies to: \[ 5x + 15 - 7x + 28 = 38 \]
-
Combine like terms on the left side: \[ (5x - 7x) + (15 + 28) = 38 \] This gives: \[ -2x + 43 = 38 \]
-
Isolate the term with \(x\) by subtracting \(43\) from both sides: \[ -2x + 43 - 43 = 38 - 43 \] This simplifies to: \[ -2x = -5 \]
-
Divide both sides by \(-2\): \[ x = \frac{-5}{-2} = \frac{5}{2} \]
Thus, the solution is: \[ x = \frac{5}{2} \quad \text{or} \quad x = 2.5 \]
1 answer