what is the absolute value of x + 3 if x is less than minus 3
Answers
I am sorry
I am weak in math
O O
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Is it true that if the absolute value of x+3 is less than 7, then x+3 = 7 and x+3 is less than -7?
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Quick tip 1: When solving an inequality, your solution will also be an inequality (If there is a solution).
Quick tip 2: When solving a linear inequality that includes an absolute value, your answer will usually be a pair of inequalities, though you may be able to combine them into a single compound inequality.
Short response:
No, but it would be true that x+3 < 7 and x+3 > -7.
Full solution:
So, you want to solve | x+3 | < 7. Since the absolute value operation takes positive or negative input and produces a positive output, you can break it apart into two separate problems:
A) (x+3) < 7
B) -(x+3) < 7
Solving A is pretty straightforward:
x+3 < 7
x < 4
To solve B, you could distribute the negative into the parentheses first, but it would probably be simpler to divide both sides by -1 first — and don't forget that anytime you multiply or divide an inequality by a negative number, it reverses the direction of the inequality sign — giving you:
x+3 > -7
x > -10
Therefore, your solution set is all values of x that are less than 4 and greater than -10, which can be written as “x < 4 and x > -10” or rearranged into a single compound inequality:
-10 < x < 4
Note that not every pair of inequalities can be combined like that; if your original problem had a >, your solution would be two linear inqualities that wouldn't overlap, and couldn't be combined.