Question

Question

Which of the following equations has a different value of x
than the others?(1 point)
Responses

x − 78 = −32
x minus Start Fraction 7 over 8 End Fraction equals negative Start Fraction 3 over 2 End Fraction

x + 0.875 = 1.5
x plus 0.875 equals 1.5

x + 98 = 74
x plus Start Fraction 9 over 8 End Fraction equals Start Fraction 7 over 4 End Fraction

x − 0.025 = 0.6

Answer 1

Let's solve each equation to find the value of \( x \):

1. Equation 1:
   \( x - 78 = -32 \)
   \( x = -32 + 78 \)
   \( x = 46 \)

2. Equation 2:
   \( x - \frac{7}{8} = -\frac{3}{2} \)
   \( x = -\frac{3}{2} + \frac{7}{8} \)
   To combine these, convert \( -\frac{3}{2} \) to eighths:
   \( -\frac{3}{2} = -\frac{12}{8} \)
   Now,
   \( x = -\frac{12}{8} + \frac{7}{8} = -\frac{5}{8} \)

3. Equation 3:
   \( x + 0.875 = 1.5 \)
   \( x = 1.5 - 0.875 \)
   Convert \( 0.875 \) to a fraction:
   \( 0.875 = \frac{7}{8}, \) so
   \( x = 1.5 - \frac{7}{8} \)
   Convert \( 1.5 \) to eighths:
   \( 1.5 = \frac{12}{8} \)
   Now,
   \( x = \frac{12}{8} - \frac{7}{8} = \frac{5}{8} \)

4. Equation 4:
   \( x - 0.025 = 0.6 \)
   \( x = 0.6 + 0.025 \)
   Convert \( 0.6 \) to a fraction:
   \( 0.6 = \frac{3}{5} \) and \( 0.025 = \frac{1}{40} \)
   To add these fractions, find a common denominator (40):
   \( \frac{3}{5} = \frac{24}{40} \)
   So,
   \( x = \frac{24}{40} + \frac{1}{40} = \frac{25}{40} = \frac{5}{8} \)

Now, we summarize the values of \( x \) from each equation:

1. Equation 1: \( x = 46 \)
2. Equation 2: \( x = -\frac{5}{8} \)
3. Equation 3: \( x = \frac{5}{8} \)
4. Equation 4: \( x = \frac{5}{8} \)

The values are:

• Equation 1: 46
• Equation 2: -0.625 (or -5/8)
• Equation 3: 0.625 (or 5/8)
• Equation 4: 0.625 (or 5/8)

Thus, Equation 1 has a different value of \( x \) than the others, which all yield either -5/8 or 5/8.

Final answer: Equation 1 (x − 78 = −32).