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$Solve for z. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. -4z+31 >= 17 z+23$

Solve for $z$ . Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. $\newline$ $-4z + 31 \geq 17z + 23$

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Solve multi-step inequalities

Full solution

Q. Solve for

z

. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.

\newline

-4z + 31 \geq 17z + 23

Rearranging the inequality: First, we want to get all the $z$ terms on one side of the inequality and the constant terms on the other side. We can do this by adding $4z$ to both sides and subtracting $23$ from both sides. $\newline$ $-4z + 31 + 4z \geq 17z + 23 + 4z$ $\newline$ $31 - 23 \geq 17z + 4z$
Simplifying the inequality: Now, we simplify both sides of the inequality by combining like terms. $\newline$ $31 - 23 = 8$ $\newline$ $17z + 4z = 21z$ $\newline$ So, we have: $\newline$ $8 \geq 21z$
Isolating z: Next, we want to isolate z by dividing both sides of the inequality by $21$ . Since we are dividing by a positive number, the direction of the inequality will not change. $\newline$ $\frac{8}{21} \geq \frac{21z}{21}$
Solution for z: After dividing, we get the solution for z. $\newline$ $\frac{8}{21} \geq z$ $\newline$ Or, we can write it as: $\newline$ $z \leq \frac{8}{21}$

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