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Sagot :
Answer:
(–2.5, ∞)
Step-by-step explanation:
Solving the Inequality
When solving for a variable in an inequality, rearrange the left and right sides like how an individual would with an equation.
We can start by distributing the 5.1 and 6 respectively,
15.3 + 11.22x > -14.25 - 10.2x - 24.
Next, we combine like terms,
15.3 + 11.22x > -38.25 - 10.2x.
We isolate all the x terms by adding 10.2x both sides (or subtracting 11.22x both sides),
21.42x + 15.3 > -38.25,
and by subtracting 15.3 both sides (or adding 38.25 both sides),
21.42x > -53.55.
Lastly, we divide both sides by the coefficient or 21.42,
x > -2.5.
Looking at all the answer choices this eliminates the top two choices:
x < -2.5 and x > 2.5.
That leaves the two interval notation answers.
Interval Notation
If a parenthesis is next to a value, whether an integer, decimal that means that the solution range excludes the value; the only exception to this are positive and negative infinity signs.
A bracket next to a value means that it includes the value.
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Reading the third answer choice (-2.5, ∞),
this indicates that the solution range starts at -2.5, excluding the value, and goes in the positive direction.
Or, on a number line, from -2.5 with an open circle to the rightward direction.
Reading the last answer choice (-∞, -2.5),
this means that the solution range goes from negative infinity up to -2.5, excluding the value itself.
Or on a number line, from the left stopping with a open circle on the value -2.5.
Looking back at our solution x > -2.5 which means all x values that are greater than -2.5 or x-values that are more positive than -2.5 like -1, 3, 5, etc., the third answer choice matches our solution's description!
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