Question

1. choose the best answer. identify the linear inequality in standard form. $2x \leq 3y + 5$ $y \geq 2x + 8$ $\frac{-2x}{5y} > 7$ $3x - 3y \geq 5$

Explanation:

Step1: Recall standard linear inequality form

The standard form of a linear inequality is $Ax + By \geq C$ (or $\leq, >, <$), where $A, B, C$ are integers, $A$ is non-negative, and there are no fractions.

Step2: Analyze each option

• Option 1: $2x \leq 3y + 5$ can be rewritten as $2x - 3y \leq 5$, but it is not in standard form as presented.
• Option 2: $y \geq 2x + 8$ can be rewritten as $2x - y \leq -8$, but it is not in standard form as presented.
• Option 3: $\frac{-2x}{5y} > 7$ is not linear (it has a variable in the denominator, making it a rational inequality).
• Option 4: $3x - 2y \geq 5$ matches the standard linear inequality form $Ax + By \geq C$, where $A=3$, $B=-2$, $C=5$, with no fractions and a non-negative leading coefficient for $x$.

Answer:

D. $3x - 2y \geq 5$