SaiBook.us SAT-2

Home Course Section

Schedule Admission Social

Step-4

Title: Linear inequalities in one or two variables

Grade: 1400-a Lesson: S1-L4

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Solve the inequality \$\sqrt (2x + 3) - 4 > 0\$.
2	Step	Add 4 to both sides of the inequality to isolate the square root term and then simplify	\$\sqrt (2x + 3) - \cancel4 + \cancel4 > 0 + 4\$ \$\sqrt (2x + 3) > 4\$
3	Step	Squaring on both sides of the inequality to eliminate the square root	\$(\sqrt (2x + 3))^2 > 4^2 \$ 2x + 3 > 16
4	Step	"Subtract 3 from both sides and divide both sides by 2:	\$2x + \cancel3 - \cancel3 > 16 - 3 \$ 2x > 13 \$ x > 13/2 \$
5	Step	Therefore, the solution to the inequality is \$ x > 13/2 \$.
6	Choice.A	This option suggests that x is greater than a negative value, which contradicts the solution \$ x > 13/2 \$	\$x > -13/2\$
7	Choice.B	This option suggests that x is less than \$13/2\$, which is the opposite of the solution \$ x > 13/2 \$	\$x < 13/2\$
8	Choice.C	This option correctly represents the solution, indicating that x is greater than \$ 13/2 \$	\$x > 13/2\$
9	Choice.D	This option suggests that x is less than a negative value, which contradicts the solution \$ x > 13/2 \$	\$x < -13/2\$
10	Answer	Option	C
11	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Solve the inequality \$\sqrt (2x + 3) - 4 > 0\$.

Step

Add 4 to both sides of the inequality to isolate the square root term and then simplify

\$\sqrt (2x + 3) - \cancel4 + \cancel4 > 0 + 4\$

\$\sqrt (2x + 3) > 4\$

Step

Squaring on both sides of the inequality to eliminate the square root

\$(\sqrt (2x + 3))^2 > 4^2 \$

2x + 3 > 16

Step

"Subtract 3 from both sides and divide both sides by 2:

\$2x + \cancel3 - \cancel3 > 16 - 3 \$

2x > 13

\$ x > 13/2 \$

Step

Therefore, the solution to the inequality is \$ x > 13/2 \$.

Choice.A

This option suggests that x is greater than a negative value, which contradicts the solution \$ x > 13/2 \$

\$x > -13/2\$

Choice.B

This option suggests that x is less than \$13/2\$, which is the opposite of the solution \$ x > 13/2 \$

\$x < 13/2\$

Choice.C

This option correctly represents the solution, indicating that x is greater than \$ 13/2 \$

\$x > 13/2\$

Choice.D

This option suggests that x is less than a negative value, which contradicts the solution \$ x > 13/2 \$

\$x < -13/2\$

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?