1

Problem

Solve the following inequality:

\$ 4x + 2y ge 6x - 3y + 2 \$

2

Step

The given inequality is

\$ 4x + 2y ge 6x - 3y + 2 \$

3

Step

Combine terms with variables on one side of inequality, then simplify:

\$ 4x - 6x + 2y + 3y ge 2 \$

\$ -2x + 5y ge 2 \$

4

Step

Divide both sides of the inequality by 5, and then simplify the expression:

\$ (- 2x + 5y) / 5 ge 2 / 5 \$

\$ (- 2)/5 x + \cancel5 / \cancel5 y ge 2/5 \$

\$ -2/5 x + y ge 2/5 \$

5

Step

Move the x variable to the right side, then a simplification:

\$ y ge 2/5 + 2/5 x \$

\$ y ge (2x + 2) / 5 \$

6

Solution

Therefore, the solution to the inequality \$4x + 2y ge 6x - 3y + 2 \$ is \$ y ge (2x + 2) / 5 \$.

7

Sumup

Please summarize steps

Choices

8

Choice-A

\$y ≥ (2x+2)/5​\$, is correct. It represents the inequality in terms of x

Correct \$ y ge (2x + 2) / 5 \$

9

Choice-B

Option B, with the inequality \$y ≥ (x + 2)/5\$​, isn’t accurate; it should feature 2x in the numerator

Wrong \$ y ge (x + 2) / 5 \$

10

Choice-C

The state \$y ≤ (2x - 2)/5\$, but our solution yields: \$y ≥ (2x + 2)/5\$, reversing the inequality

Wrong \$ y le (2x - 2) / 5 \$

11

Choice-D

The inequality \$y ≤ (2x+1)/3\$ is incorrect; it should be \$y ≥ (2x+1)/3\$, as the expression varies

Wrong \$ y le (2x + 1) / 3 \$

12

Answer

Option

A

13

Sumup

Please summarize choices