Solve each equation. Type the answers in the boxes below. 1. \( -\frac{1}{8} d-4=-\frac{3}{8} \) d \( =-\frac{1}{4} m+5=16 \) \( m= \) 3. \( 10 b+-45=-43 \) \( b= \)
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To solve the equations: 1. Starting with the equation \(-\frac{1}{8} d - 4 = -\frac{3}{8}\), we first add 4 to both sides. To do this, convert 4 to eighths: \(4 = \frac{32}{8}\). Thus, we get: \[ -\frac{1}{8} d = -\frac{3}{8} + \frac{32}{8} = \frac{29}{8} \] Now, to isolate \(d\), multiply both sides by -8: \[ d = -8 \cdot \frac{29}{8} = -29 \] 2. For the second equation \(-\frac{1}{4} m + 5 = 16\), we subtract 5 from both sides: \[ -\frac{1}{4} m = 16 - 5 = 11 \] Multiply both sides by -4 to isolate \(m\): \[ m = -4 \cdot 11 = -44 \] 3. Finally, for \(10b - 45 = -43\), we add 45 to both sides: \[ 10b = -43 + 45 = 2 \] To find \(b\), divide by 10: \[ b = \frac{2}{10} = \frac{1}{5} \] The answers are: \( d = -29 \) \( m = -44 \) \( b = \frac{1}{5} \)
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