Solve the linear inequality. Other than ∅, use interval notation to express the solution set and graph the solution set
on a number line.
-$y = 6 - 2 ( 2 - x )$ and $y$ is at most 10 .
A) $( - \infty , 4 ]$
B) $[ 4 , \infty )$
C) $( - \infty , 5 ]$
D) $( - \infty , 4 )$

Question

Quizplus · Accepted Answer

First, solve the equation $y = 6 - 2(2 - x)$ for $x$. Distributing the -2 gives $y = 6 - 4 + 2x$, which simplifies to $y = 2 + 2x$. Rearranging for $x$, we get $x = \frac{y - 2}{2}$. Setting $y \leq 10$, we solve for $x$ to get $x \leq 4$, which corresponds to the interval $(- \infty , 4 ]$.

Solve the Linear Inequality y=6−2(2−x)y = 6 - 2 ( 2 - x )y=6−2(2−x)

Solve the Linear Inequality $y = 6 - 2 ( 2 - x )$