Solve the following inequality: \$ 4x + 2y ge 6x - 3y + 2 \$.

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

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

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

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

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

\$ (- 2x)/5 + (\cancel5y)/\cancel5 ge 2/5 \$

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

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

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

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

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

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

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

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

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

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

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

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

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

Option

A

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