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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. \( 10 b+-45=-43 \) \( b= \)

Ask by Reid Daniel. in the United States
Mar 09,2025

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Tutor-Verified Answer

Answer

\( d = -29 \), \( m = -44 \), \( b = 0.2 \).

Solution

Solve the equation by following steps: - step0: Solve for \(b\): \(10b-45=-43\) - step1: Move the constant to the right side: \(10b=-43+45\) - step2: Add the numbers: \(10b=2\) - step3: Divide both sides: \(\frac{10b}{10}=\frac{2}{10}\) - step4: Divide the numbers: \(b=\frac{1}{5}\) Solve the equation \( -\frac{1}{4} m + 5 = 16 \). Solve the equation by following steps: - step0: Solve for \(m\): \(-\frac{1}{4}m+5=16\) - step1: Move the constant to the right side: \(-\frac{1}{4}m=16-5\) - step2: Subtract the numbers: \(-\frac{1}{4}m=11\) - step3: Change the signs: \(\frac{1}{4}m=-11\) - step4: Multiply by the reciprocal: \(\frac{1}{4}m\times 4=-11\times 4\) - step5: Multiply: \(m=-44\) Solve the equation \( -\frac{1}{8} d - 4 = -\frac{3}{8} \). Solve the equation by following steps: - step0: Solve for \(d\): \(-\frac{1}{8}d-4=-\frac{3}{8}\) - step1: Move the constant to the right side: \(-\frac{1}{8}d=-\frac{3}{8}+4\) - step2: Add the numbers: \(-\frac{1}{8}d=\frac{29}{8}\) - step3: Change the signs: \(\frac{1}{8}d=-\frac{29}{8}\) - step4: Multiply by the reciprocal: \(\frac{1}{8}d\times 8=-\frac{29}{8}\times 8\) - step5: Multiply: \(d=-29\) Here are the solutions for each equation: 1. For the equation \( -\frac{1}{8} d - 4 = -\frac{3}{8} \): \[ d = -29 \] 2. For the equation \( -\frac{1}{4} m + 5 = 16 \): \[ m = -44 \] 3. For the equation \( 10 b - 45 = -43 \): \[ b = 0.2 \] You can fill in the answers as follows: - \( d = -29 \) - \( m = -44 \) - \( b = 0.2 \)

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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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