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Solve for $z$ . $\newline$ $3z - 2 \geq 4$

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Solve two-step inequalities

Full solution

Q. Solve for

z

.

\newline

3z - 2 \geq 4

Isolate variable z: Start by isolating the variable z on one side of the inequality. $\newline$ We have the inequality $3z - 2 \geq 4$ . $\newline$ To isolate z, we need to add $2$ to both sides of the inequality. $\newline$ $3z - 2 + 2 \geq 4 + 2$ $\newline$ This simplifies to: $\newline$ $3z \geq 6$
Divide by $3$ : Now, divide both sides of the inequality by $3$ to solve for $z$ . $\frac{3z}{3} \geq \frac{6}{3}$ This simplifies to: $z \geq 2$
Check solution: Check the solution to ensure it makes sense. $\newline$ If we substitute $z$ with a number greater than or equal to $2$ back into the original inequality, it should hold true. $\newline$ Let's test $z = 2$ : $\newline$ $3(2) - 2 \geq 4$ $\newline$ $6 - 2 \geq 4$ $\newline$ $4 \geq 4$ $\newline$ This is true, so our solution is correct.

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