Question

Celia uses the steps below to solve the equation Negative StartFraction 3 over 8 EndFraction (negative 8 minus 16 d) + 2 d = 24.


Step 1 Distribute Negative StartFraction 3 over 8 EndFraction over the expression in parentheses.
3 minus 16 d + 2 d = 24
Step 2 Simplify like terms.
3 minus 14 d = 24
Step 3 Subtract 3 from both sides of the equation.
Negative 14 d = 21
Step 4 Divide both sides of the equation by –14.
d = StartFraction 21 over negative 14 EndFraction = Negative three-halves = negative 1 and one-half

Which corrects the error in the step in which Celia made the first error?
In step 1, she should have also distributed Negative StartFraction 3 over 8 EndFraction over 2d, to get 3 minus 16 d + (negative three-fourths d) = 24.
In step 1, she should have also distributed Negative StartFraction 3 over 8 EndFraction over –16d, to get 3 + 6 d + 2 d = 24.
In step 3, she should have added 3 to both sides of the equation to get Negative 14 d = 27.
In step 3, she should have first divided both sides by –14 to get 3 + d = 24

Answer 1

The error in the steps is that In step 1, she should have also distributed -3/8  over –16d, to get 3 + 6 d + 2 d = 24

Simplifying linear equations

Given the following equation as shown below

-3/8(-8-16d)+2d = 24

Step 1 Distribute -3/8 over the expression in parentheses

3 + 6d + 2d = 24

Simply the like terms

3 + 8d = 24

Subtract 3 from both sides of the equation.

8d = 24 - 3

8d = 21

d = 21/8

Hence the error in the steps is that In step 1, she should have also distributed -3/8  over –16d, to get 3 + 6 d + 2 d = 24

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