Solve for z. 20 ≤ 8(z + 19) + 4 ______

Distribute 8: First, we need to simplify the inequality by distributing the 8 across the terms inside the parentheses. 20 ≤ 8(z + 19) + 4 20 ≤ 8z + 8(19) + 4Calculate product: Now, we calculate the product of 8 and 19. 20 ≤ 8z + 152 + 4Combine constant terms: Next, we combine the constant terms on the right side of the inequality. 20 ≤ 8z + 156Isolate variable term: To isolate the variable term, we subtract 156 from both sides of the inequality. 20 - 156 ≤ 8z + 156 - 156 -136 ≤ 8zDivide to solve for z: Finally, we divide both sides of the inequality by 8 to solve for z. -136/8 ≤ 8z/8 -17 ≤ z

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Math Problems

Algebra 1

Solve advanced linear inequalities

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Q. Solve for

z

\newline

20 \leq 8(z + 19) + 4

Distribute $8$ : First, we need to simplify the inequality by distributing the $8$ across the terms inside the parentheses. $\newline$ $20 \leq 8(z + 19) + 4$ $\newline$ $20 \leq 8z + 8(19) + 4$
Calculate product: Now, we calculate the product of $8$ and $19$ . $\newline$ $20 \leq 8z + 152 + 4$
Combine constant terms: Next, we combine the constant terms on the right side of the inequality. $20 \leq 8z + 156$
Isolate variable term: To isolate the variable term, we subtract $156$ from both sides of the inequality. $\newline$ $20 - 156 \leq 8z + 156 - 156$ $\newline$ $-136 \leq 8z$
Divide to solve for z: Finally, we divide both sides of the inequality by $8$ to solve for $z$ . $\newline$ $\frac{-136}{8} \leq \frac{8z}{8}$ $\newline$ $-17 \leq z$