Ask a New Question
Menu

Suzie solved the equation 9x−5=14(16x+60) using the following steps:

1) Distribute 1/4 to get 9x−5=4x+60

2) Use subtraction property of equality to move 4x to get 5x−5=60

3) Use addition property of equality to move 5 and get 5x=65

4) Use division property of equality to get x=13

Determine if Suzie solved correctly - if not, identify which step was the mistake.

(1 point)
Responses

Suzie made a mistake on Step 4 - she divided incorrectly
Suzie made a mistake on Step 4 - she divided incorrectly

Suzie solved the problem correctly
Suzie solved the problem correctly

Suzie made a mistake on Step 1 - she should have distributed the 1/4 to 60 as well
Suzie made a mistake on Step 1 - she should have distributed the 1/4 to 60 as well

Suzie made a mistake on Step 2 - she should have used the addition property instead
Suzie made a mistake on Step 2 - she should have used the addition property instead

1 answer

To determine if Suzie solved the equation correctly, let's review her steps and identify any mistakes.

The original equation is: \[ 9x - 5 = 14(16x + 60) \]

  1. Suzie claims to have distributed \( \frac{1}{4} \) to get: \[ 9x - 5 = 4x + 60 \] This is incorrect. The correct distribution should be: \[ 14(16x + 60) = 224x + 840 \] So, the equation becomes: \[ 9x - 5 = 224x + 840 \]

  2. If we argue the subtraction step from her incorrect result in Step 1: Then she should have moved \( 224x \) instead, leading to: \[ 9x - 224x - 5 = 840 \] This simplifies to: \[ -215x - 5 = 840 \]

  3. Adding 5 to both sides gives: \[ -215x = 845 \]

  4. Dividing both sides by -215: \[ x = -\frac{845}{215} \] Simplifying this gives: \[ x = -\frac{169}{43} \]

Thus, Suzie made an error in Step 1 when distributing incorrectly. Therefore, the correct response is:

Suzie made a mistake on Step 1 - she should have distributed correctly to both terms inside the parentheses.