Determine whether each value of x is a solution of the...

Determine whether each value of $x$ is a solution of the inequality. (Values) (a) $x=3 \quad$ (b) $x=-3$ (c) $x=\frac{5}{2} \quad$ (d) $x=\frac{3}{2}$ (a) $x=-\frac{1}{2} \quad$ (b) $x=-\frac{5}{2}$ (c) $x=\frac{4}{3} \quad$ (d) $x=0$ (a) $x=-1 \quad$ (b) $x=\sqrt{5}$ (c) $x=1 \quad$ (d) $x=5$ (a) $x=13 \quad$ (b) $x=-1$ (c) $x=14 \quad$ (d) $x=8$ $$5 x-12>0$$

Determine whether each value of $x$ is a solution of the inequality.
(Values)
(a) $x=3 \quad$ (b) $x=-3$
(c) $x=\frac{5}{2} \quad$ (d) $x=\frac{3}{2}$
(a) $x=-\frac{1}{2} \quad$ (b) $x=-\frac{5}{2}$
(c) $x=\frac{4}{3} \quad$ (d) $x=0$
(a) $x=-1 \quad$ (b) $x=\sqrt{5}$
(c) $x=1 \quad$ (d) $x=5$
(a) $x=13 \quad$ (b) $x=-1$
(c) $x=14 \quad$ (d) $x=8$
$$5 x-12>0$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Solution Set

The solution set of an inequality is the complete set of values that satisfy the condition imposed by the inequality. It is usually expressed in interval notation or as a set of numbers that meet the required criteria from the inequality.

Substitution Method

The substitution method entails plugging in candidate values into the inequality to check if they make the inequality true. This direct verification is especially useful when a list of specific values is provided to determine which ones belong to the solution set.

Linear Inequality

A linear inequality is an inequality that involves a linear expression, where the variable is to the first power. The process to solve such an inequality is similar to solving a linear equation, but care must be taken when multiplying or dividing by negative numbers, as that reverses the inequality sign.

Critical Value

The critical value is the point at which the expression in the inequality equals zero, thus serving as a boundary between values that satisfy the inequality and those that do not. This value is often determined by solving the equation obtained by replacing the inequality sign with an equality.

Transcript

00:02 If we're given the inequality, 5x minus 12 is greater than zero, and we're given some solutions, and we want to verify whether or not the solutions are correct.

00:13 We can use substitution to do that.

00:16 So this first one, we're given x equals three.

00:21 This one here, we're given x equals negative three.

00:25 This one, we're given x equals five halves.

00:29 And over here, we're given x equals three halves.

00:31 So we have these four solutions, and we're going to determine whether each value of x, is actually a solution to the inequality, 5x minus 12 is greater than 0.

00:43 So on this one, x equals 3, 5 times 3 minus 12 is greater than 0.

00:49 5 times 3 is 15 minus 12 is greater than 0.

00:55 And we get 3 is greater than 0.

00:57 3 is in fact greater than 0.

00:59 So x equals 3 is a solution to this inequality.

01:04 Our second choice, negative 3, 5 times 0 ,000.

01:07 Negative 3 minus 12 is greater than 0.

01:11 5 times negative 3 is negative 15 minus 12 is greater than 0.

01:16 And we get negative 27 is greater than 0.

01:19 Negative 27 is not greater than 0.

01:22 This is not a true statement.

01:23 So x equals negative 3 is not a solution to this inequality...