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Solve each inequality. Write the solution set in interval notation and graph it.$$3-x<5<7-x$$
$x \in(-2,2)$
Precalculus
Algebra
Chapter 2
Equations, Inequalities, and Problem Solving
Section 7
Solving Inequalities
Algebra Topics That are Reviewed at the Start of the Semester
Equations and Inequalities
Campbell University
Baylor University
Lectures
01:32
In mathematics, the absolu…
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01:10
Solve each inequality. Gra…
01:42
01:18
Solve each compound inequa…
01:28
Solve each inequality. Wri…
03:16
01:46
00:56
01:27
02:10
02:11
solve the compound inequality three minus X is less than five is less than seven minus X. To solve a compound inequality, we need to isolate the variable in the middle part of the compound inequality. To do this, let's move the negative x from three minus x into the middle part of the inequality by adding X. If we add X, we must do it to all parts of the inequality. Keep it true, so add X to all three parts of the inequality. Three minus X plus X is three is less than five plus X is less fan seven minus X plus X, which is seven toe isolate x by itself, in the middle of the inequality, we need to undo the addition of five. So we're going to subtract five from all three parts of the inequality. Three. Minus five is negative two, which is less than five plus X minus five, which is X, and that is less than seven minus five, which is positive, too. Our solution set includes all values that are greater than negative, too, and less than positive, too. An interval notation will open the interval with a parentheses at negative two and closed the interval at two, Also with a parentheses. E. We use the parentheses E to indicate that the endpoint values are not included in the solution set on our number line. We will have an open circle at negative two and an open circle at positive two. We want to shade the region of values that is between negative to into so on. Our number lines the shade between the two endpoints.
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