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Jordan solved the equation −7x + 25 = 48; his work is shown below. Identify the error and where it was made. −7x + 25 = 48 Step 1: −7x + 25 − 25 = 48 − 25 Step 2: −7x = 23 Step 3: negative seven times x over seven = twenty-three over seven Step 4: x = twenty-three over seven

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Kaneki0Ken

the problem seems to be correct there should be there aren't any mistakes right?

sebasgadu

Answer:

The error was that Jordan didn't take into account the minus sign in the step 3. The solution of the equation is \(x=-\frac{23}{7}\)

Step-by-step explanation:

The steps to solve the equation \(-7x+25=48\) would be:

  1. \(-7x+25-25=48-25\),          the step 1 is correct.
  2. \(-7x=23\),          the step 2 is correct
  3. \(\frac{-7x}{7}=\frac{23}{7}\),          the step 3 is correct.
  4. \(x=\frac{23}{7}\),           the step 4 is INCORRECT

The step 4 is incorrect because the minus sign in the step 3 was not taken into account. The correct steps would be:

  1. \(-7x+25-25=48-25\)
  2. \(-7x=23\)
  3. \(\frac{-7x}{7}=\frac{23}{7}\)
  4. \(-x=\frac{23}{7}\)
  5. \(-x\cdot (-1)=\frac{23}{7}\cdot (-1)\)
  6. \(x=-\frac{23}{7}\)

Thus, the error was that Jordan didn't take into account the minus sign in the step 3. The solution of the equation is \(x=-\frac{23}{7}\)

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