Can one of the inequalities be written as the other?
No
Practice makes perfect
Let's begin by stating the inequalities.
lc45 ≤ - 5 +z & (I) 40 ≤ z & (II)
If two inequalities are equivalent, it is possible to write one of them as the other. To determine if the given inequalities are equivalent, we will attempt to write Inequality (I) as Inequality (II).
When the variable in Inequality (I) is isolated, we see that the two inequalities are not the same. Therefore, they are not equivalent.
Extra
Why It Works?
Let's focus on why we could add 5 to both sides of the inequality. First, we will recall the Addition Property of Inequality.
Addition Property of Inequality
Adding the same number to both sides of an inequality creates an equivalent inequality. This equivalent inequality will have the same solution as the original inequality.
This means that adding 5 to both sides of the equation deos not change the solutions of the inequality. Next, let's think about what we could change in the first inequality to make inequalities equivalent. We will begin by replacing -5 with a variable, x.
lc45 ≤ x +z & (I) 40 ≤ z & (II)
Next, let's recall the Subtraction Property of Inequality.
Subtraction Property of Inequality
Subtracting the same number from both sides of an inequality creates an equivalent inequality. This equivalent inequality will have the same solution as the original inequality.
Because of this we can subtract x from both sides of the inequality (I). If the left-hand side of the inequality (I) will be equal to the left hand-side of the inequality (II) the inequalities will be equivalent. Let's do this!
