Consider the equation \( 17-3 x=-\left(12-\frac{5}{8} x\right) \). beta Which is the solution?

To solve the equation \( 17 - 3x = -\left(12 - \frac{5}{8}x\right) \), let's start by distributing the negative on the right side: \[ 17 - 3x = -12 + \frac{5}{8}x. \] Now, add \( 3x \) to both sides and add \( 12 \) to both sides to isolate \( x \): \[ 17 + 12 = 3x + \frac{5}{8}x \] \[ 29 = 3x + \frac{5}{8}x. \] To combine like terms, convert \( 3x \) to eighths: \[ 3x = \frac{24}{8}x, \] which gives us: \[ 29 = \frac{24}{8}x + \frac{5}{8}x \] \[ 29 = \frac{29}{8}x. \] Now, multiply both sides by \( \frac{8}{29} \): \[ x = 29 \times \frac{8}{29} \] \[ x = 8. \] So, the solution is \( x = 8 \). Now, let’s look at how to apply this in the real world: You could be solving problems related to budgeting, where you set up equations to express income and expenses. Work through them like this equation, simplifying and isolating variables to find your final amounts. Also, when solving equations, one common mistake is to forget to distribute the negative sign properly or to miss combining like terms. Always double-check your steps to ensure everything balances out correctly!