Answer:
see attached
Explanation:
You are given two solutions to a 3-step inequality and are asked to describe them.
3-Step inequality
These inequalities have variable terms and constant terms on both sides of the comparison symbol. The expressions have been simplified.
These inequalities can be described as 3-step, because a straightforward solution can be accomplished in 3 steps. The first two steps separate the constant and variable terms, and the final step divides by the coefficient of the variable.
The process is virtually identical to that for solving a 3-step equation.
Allison
Allison's first step is to get rid of one of the unwanted variable terms by subtracting it from both sides. She chose the "3x" term, which has a smaller coefficient than the "5x" term, so the resulting difference will leave a positive coefficient on the x-term.
Then she removed the unwanted constant from the side with 2x by adding its opposite.
Since the x-term has a positive coefficient, Allison did not have to change anything about the inequality symbol when she divide both sides by that coefficient.
John
John used a first step similar to Allison's but he chose to eliminate the 5x term. The result was the x-term ended up with a negative coefficient. That introduces an extra bit of procedure at the end when he divides by the -2 coefficient of x: the inequality symbol must be reversed.
The constant term on the side with the x-term was removed by adding its opposite. This is the same step Allison performed as step 2.
When John finally divides by the coefficient of x, he has to reverse the inequality symbol, since that coefficient is negative.
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Additional comment
You can compare one line of the solution to the one above to see what is different. Identifying that difference will tell you what step was taken to get the current line from the previous one. It helps to understand the way equations and inequalities are solved, so you better know what to look for.