Question

solve each equation. list your answer(s) as a set.

1. 9| -5b + 10| - 2 = 88
2. 9|6d - 1| - 9 = -18
3. 4|6 - 4x| - 4 = -20
4. 9 - 7|1 - 3x| = 37

Explanation:

Step1: Solve equation 3) \( 9| -5b + 10 | - 2 = 88 \)

First, isolate the absolute value expression. Add 2 to both sides:
\( 9| -5b + 10 | = 88 + 2 = 90 \)
Divide both sides by 9:
\( | -5b + 10 | = \frac{90}{9} = 10 \)

Now, split into two cases for the absolute value:
Case 1: \( -5b + 10 = 10 \)
Subtract 10 from both sides: \( -5b = 0 \)
Divide by -5: \( b = 0 \)

Case 2: \( -5b + 10 = -10 \)
Subtract 10 from both sides: \( -5b = -20 \)
Divide by -5: \( b = 4 \)

Step2: Solve equation 4) \( 9|6t - 1| - 9 = -18 \)

Isolate the absolute value: Add 9 to both sides:
\( 9|6t - 1| = -18 + 9 = -9 \)
Divide by 9: \( |6t - 1| = \frac{-9}{9} = -1 \)

Absolute value cannot be negative, so no solution (since \( |x| \geq 0 \) for all real \( x \)).

Step3: Solve equation 5) \( 4|6 - 4x| - 4 = -40 \)

Isolate the absolute value: Add 4 to both sides:
\( 4|6 - 4x| = -40 + 4 = -36 \)
Divide by 4: \( |6 - 4x| = \frac{-36}{4} = -9 \)

Absolute value cannot be negative, so no solution (since \( |x| \geq 0 \) for all real \( x \)).

Step4: Solve equation 6) \( 9 - 7|1 - 3x| = 37 \)

Isolate the absolute value: Subtract 9 from both sides:
\( -7|1 - 3x| = 37 - 9 = 28 \)
Divide by -7: \( |1 - 3x| = \frac{28}{-7} = -4 \)

Absolute value cannot be negative, so no solution (since \( |x| \geq 0 \) for all real \( x \)).

Answer:

• Equation 3: \( \{0, 4\} \)
• Equation 4: No solution
• Equation 5: No solution
• Equation 6: No solution