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Which of the following equations has a different value of x than the others?(1 point) Responses x + 9/8 = 7/4 x plus Start Fraction 9 over 8 End Fraction equals Start Fraction 7 over 4 End Fraction x + 0.875 = 1.5 x plus 0.875 equals 1.5 x − 0.025 = 0.6 x minus 0.025 equals 0.6 x − 7/8 = −3/2

3 answers

To determine which equation has a different value of \( x \), we'll solve each equation step by step:

  1. Equation 1:
    \( x + \frac{9}{8} = \frac{7}{4} \)
    Convert \( \frac{7}{4} \) into eighths:
    \( \frac{7}{4} = \frac{14}{8} \)
    Now, the equation is:
    \( x + \frac{9}{8} = \frac{14}{8} \)
    Subtract \( \frac{9}{8} \) from both sides:
    \( x = \frac{14}{8} - \frac{9}{8} = \frac{5}{8} \)

  2. Equation 2:
    \( x + 0.875 = 1.5 \)
    Convert 0.875 and 1.5 to fractions:
    \( 0.875 = \frac{7}{8} \) and \( 1.5 = \frac{3}{2} = \frac{12}{8} \)
    Now, the equation is:
    \( x + \frac{7}{8} = \frac{12}{8} \)
    Subtract \( \frac{7}{8} \) from both sides:
    \( x = \frac{12}{8} - \frac{7}{8} = \frac{5}{8} \)

  3. Equation 3:
    \( x - 0.025 = 0.6 \)
    Convert \( 0.6 \) into a fraction:
    \( 0.6 = \frac{3}{5} \)
    So, we have:
    \( x - 0.025 = \frac{3}{5} \)
    Add \( 0.025 \) (which is \( \frac{1}{40} \)) to both sides:
    \( x = \frac{3}{5} + 0.025 \)
    Convert \( \frac{3}{5} \) to a fraction with a common denominator of 40:
    \( \frac{3}{5} = \frac{24}{40} \)
    Therefore,
    \( x = \frac{24}{40} + \frac{1}{40} = \frac{25}{40} = \frac{5}{8} \)

  4. Equation 4:
    \( x - \frac{7}{8} = -\frac{3}{2} \)
    Convert \( -\frac{3}{2} \) into eighths:
    \( -\frac{3}{2} = -\frac{12}{8} \)
    Now, the equation is:
    \( x - \frac{7}{8} = -\frac{12}{8} \)
    Add \( \frac{7}{8} \) to both sides:
    \( x = -\frac{12}{8} + \frac{7}{8} = -\frac{5}{8} \)

Now we can summarize the values we've found:

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

The equation that has a different value of \( x \) is Equation 4, which gives \( x = -\frac{5}{8} \).

wrong chose one of these
x + 9/8 = 7/4
x + 0.875 = 1.5
x - 0.025 = 0.6
x - 7/8 = -3/2

Let's re-evaluate the equations one by one to find which one has a different value for \( x \):

  1. Equation 1:
    \( x + \frac{9}{8} = \frac{7}{4} \)
    Convert \( \frac{7}{4} \) to eighths:
    \( \frac{7}{4} = \frac{14}{8} \)
    So,
    \( x + \frac{9}{8} = \frac{14}{8} \)
    Subtract \( \frac{9}{8} \) from both sides:
    \( x = \frac{14}{8} - \frac{9}{8} = \frac{5}{8} \)

  2. Equation 2:
    \( x + 0.875 = 1.5 \)
    Convert 0.875 and 1.5 into fractions:
    \( 0.875 = \frac{7}{8} \) and \( 1.5 = \frac{3}{2} = \frac{12}{8} \)
    Then, the equation becomes:
    \( x + \frac{7}{8} = \frac{12}{8} \)
    Subtract \( \frac{7}{8} \):
    \( x = \frac{12}{8} - \frac{7}{8} = \frac{5}{8} \)

  3. Equation 3:
    \( x - 0.025 = 0.6 \)
    Convert \( 0.6 \) to a fraction:
    \( 0.6 = \frac{3}{5} \)
    So, rewrite the equation:
    \( x - 0.025 = \frac{3}{5} \)
    Add \( 0.025 \) to both sides:
    Since \( 0.025 = \frac{1}{40} \), we will need a common denominator:
    \( \frac{3}{5} = \frac{24}{40} \)
    Therefore,
    \( x = \frac{24}{40} + \frac{1}{40} = \frac{25}{40} = \frac{5}{8} \)

  4. Equation 4:
    \( x - \frac{7}{8} = -\frac{3}{2} \)
    Convert \( -\frac{3}{2} \) to eighths:
    \( -\frac{3}{2} = -\frac{12}{8} \)
    So,
    \( x - \frac{7}{8} = -\frac{12}{8} \)
    Add \( \frac{7}{8} \):
    \( x = -\frac{12}{8} + \frac{7}{8} = -\frac{5}{8} \)

Now we summarize the values found:

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

The equation that has a different value of \( x \) than the others is Equation 4: \( x - \frac{7}{8} = -\frac{3}{2} \) which gives \( x = -\frac{5}{8} \).