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Solve for $z$ . $\newline$ $-3 + 2z \leq 5$

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Solve two-step inequalities

Full solution

Q. Solve for

z

.

\newline

-3 + 2z \leq 5

Isolate variable $z$ : Start by isolating the variable $z$ on one side of the inequality. $\newline$ Add $3$ to both sides of the inequality to cancel out the $-3$ on the left side. $\newline$ $-3 + 2z + 3 \leq 5 + 3$ $\newline$ $2z \leq 8$
Add $3$ to both sides: Divide both sides of the inequality by $2$ to solve for $z$ . $\frac{2z}{2} \leq \frac{8}{2}$ $z \leq 4$
Divide by $2$ : Check the solution by plugging the value of $z$ back into the original inequality to ensure it makes the inequality true. $\newline$ Let's check if $z = 4$ satisfies the inequality $-3 + 2z \leq 5$ . $\newline$ $-3 + 2(4) \leq 5$ $\newline$ $-3 + 8 \leq 5$ $\newline$ $5 \leq 5$ $\newline$ Since $5$ is equal to $5$ , the inequality holds true.

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