15) - 5 - 5(m - 8)=4m - 19 16) - 3(6m + 6)+4m=-8m + 24 17) -(m + 3)=-6m - 13 18) - 6+2(x + 2)=28 + 8x 19) 15 - 2n=-5(n - 3) 20) -(-6x + 2)=-10 + 4x 21) r - 1+r - 5=-2(r - 1)+3(-4) 22) 3p - 4(p + 7)=4(2p - 7) 23) - 6(b + 9)≥66 24) 7(n + 4)-81 27) - 2+8p-8(1 - p) 28) - 32+3b-4(-3b + 8) 29) 4(x + 2)≥-7 + x 30) 3(1 + 6m)+6≥35 + 5m solve each inequality.

Question

15) - 5 - 5(m - 8)=4m - 19
16) - 3(6m + 6)+4m=-8m + 24
17) -(m + 3)=-6m - 13
18) - 6+2(x + 2)=28 + 8x
19) 15 - 2n=-5(n - 3)
20) -(-6x + 2)=-10 + 4x
21) r - 1+r - 5=-2(r - 1)+3(-4)
22) 3p - 4(p + 7)=4(2p - 7)
23) - 6(b + 9)≥66
24) 7(n + 4)<-42
25) (\frac{x}{3}+4leq4)
26) 7m + 3>-81
27) - 2+8p>-8(1 - p)
28) - 32+3b>-4(-3b + 8)
29) 4(x + 2)≥-7 + x
30) 3(1 + 6m)+6≥35 + 5m
solve each inequality.

Accepted Answer

15. # Explanation: ## Step1: Expand the equation $$ \begin{align*} -5 - 5(m - 8)&=4m-19\ -5-5m + 40&=4m-19 \end{align*} $$ ## Step2: Combine like - terms $$ \begin{align*} 35-5m&=4m-19 \end{align*} $$ ## Step3: Add $5m$ to both sides $$ \begin{align*} 35&=4m + 5m-19\ 35&=9m-19 \end{align*} $$ ## Step4: Add 19 to both sides $$ \begin{align*} 35 + 19&=9m\ 54&=9m \end{align*} $$ ## Step5: Solve for $m$ $$ \begin{align*} m&=\frac{54}{9}\ m& = 6 \end{align*} $$ # Answer: $m = 6$ 16. # Explanation: ## Step1: Expand the equation $$ \begin{align*} -3(6m + 6)+4m&=-8m + 24\ -18m-18 + 4m&=-8m + 24 \end{align*} $$ ## Step2: Combine like - terms $$ \begin{align*} -14m-18&=-8m + 24 \end{align*} $$ ## Step3: Add $14m$ to both sides $$ \begin{align*} -18&=-8m+14m + 24\ -18&=6m + 24 \end{align*} $$ ## Step4: Subtract 24 from both sides $$ \begin{align*} -18-24&=6m\ -42&=6m \end{align*} $$ ## Step5: Solve for $m$ $$ \begin{align*} m&=\frac{-42}{6}\ m&=-7 \end{align*} $$ # Answer: $m=-7$ 17. # Explanation: ## Step1: Expand the equation $$ \begin{align*} -(m + 3)&=-6m-13\ -m-3&=-6m-13 \end{align*} $$ ## Step2: Add $6m$ to both sides $$ \begin{align*} -m+6m-3&=-13\ 5m-3&=-13 \end{align*} $$ ## Step3: Add 3 to both sides $$ \begin{align*} 5m&=-13 + 3\ 5m&=-10 \end{align*} $$ ## Step4: Solve for $m$ $$ \begin{align*} m&=\frac{-10}{5}\ m&=-2 \end{align*} $$ # Answer: $m=-2$ 18. # Explanation: ## Step1: Expand the equation $$ \begin{align*} -6+2(x + 2)&=28+8x\ -6 + 2x+4&=28+8x \end{align*} $$ ## Step2: Combine like - terms $$ \begin{align*} 2x-2&=28+8x \end{align*} $$ ## Step3: Subtract $2x$ from both sides $$ \begin{align*} -2&=28+8x-2x\ -2&=28 + 6x \end{align*} $$ ## Step4: Subtract 28 from both sides $$ \begin{align*} -2-28&=6x\ -30&=6x \end{align*} $$ ## Step5: Solve for $x$ $$ \begin{align*} x&=\frac{-30}{6}\ x&=-5 \end{align*} $$ # Answer: $x=-5$ 19. # Explanation: ## Step1: Expand the equation $$ \begin{align*} 15-2n&=-5(n - 3)\ 15-2n&=-5n + 15 \end{align*} $$ ## Step2: Add $5n$ to both sides $$ \begin{align*} 15-2n+5n&=15\ 15 + 3n&=15 \end{align*} $$ ## Step3: Subtract 15 from both sides $$ \begin{align*} 3n&=15 - 15\ 3n&=0 \end{align*} $$ ## Step4: Solve for $n$ $$ \begin{align*} n&=\frac{0}{3}\ n&=0 \end{align*} $$ # Answer: $n = 0$ 20. # Explanation: ## Step1: Expand the equation $$ \begin{align*} -(-6x + 2)&=-10+4x\ 6x-2&=-10 + 4x \end{align*} $$ ## Step2: Subtract $4x$ from both sides $$ \begin{align*} 6x-4x-2&=-10\ 2x-2&=-10 \end{align*} $$ ## Step3: Add 2 to both sides $$ \begin{align*} 2x&=-10 + 2\ 2x&=-8 \end{align*} $$ ## Step4: Solve for $x$ $$ \begin{align*} x&=\frac{-8}{2}\ x&=-4 \end{align*} $$ # Answer: $x=-4$ 21. # Explanation: ## Step1: Expand the equation $$ \begin{align*} r-1+r-5&=-2(r - 1)+3(-4)\ 2r-6&=-2r + 2-12 \end{align*} $$ ## Step2: Combine like - terms $$ \begin{align*} 2r-6&=-2r-10 \end{align*} $$ ## Step3: Add $2r$ to both sides $$ \begin{align*} 2r+2r-6&=-10\ 4r-6&=-10 \end{align*} $$ ## Step4: Add 6 to both sides $$ \begin{align*} 4r&=-10 + 6\ 4r&=-4 \end{align*} $$ ## Step5: Solve for $r$ $$ \begin{align*} r&=\frac{-4}{4}\ r&=-1 \end{align*} $$ # Answer: $r=-1$ 22. # Explanation: ## Step1: Expand the equation $$ \begin{align*} 3p-4(p + 7)&=4(2p-7)\ 3p-4p-28&=8p-28 \end{align*} $$ ## Step2: Combine like - terms $$ \begin{align*} -p-28&=8p-28 \end{align*} $$ ## Step3: Add $p$ to both sides $$ \begin{align*} -28&=8p + p-28\ -28&=9p-28 \end{align*} $$ ## Step4: Add 28 to both sides $$ \begin{align*} 0&=9p \end{align*} $$ ## Step5: Solve for $p$ $$ \begin{align*} p&=\frac{0}{9}\ p&=0 \end{align*} $$ # Answer: $p = 0$ 23. # Explanation: ## Step1: Expand the inequality $$ \begin{align*} -6(b + 9)&\geq66\ -6b-54&\geq66 \end{align*} $$ ## Step2: Add 54 to both sides $$ \begin{align*} -6b&\geq66 + 54\ -6b&\geq120 \end{align*} $$ ## Step3: Divide both sides by $-6$ and reverse the inequality sign $$ \begin{align*} b&\leq\frac{120}{-6}\ b&\leq - 20 \end{align*} $$ # Answer: $b\leq - 20$ 24. # Explanation: ## Step1: Expand the inequality $$ \begin{align*} 7(n + 4)&\lt-42\ 7n+28&\lt-42 \end{align*} $$ ## Step2: Subtract 28 from both sides $$ \begin{align*} 7n&\lt-42-28\ 7n&\lt-70 \end{align*} $$ ## Step3: Divide both sides by 7 $$ \begin{align*} n&\lt\frac{-70}{7}\ n&\lt - 10 \end{align*} $$ # Answer: $n\lt - 10$ 25. # Explanation: ## Step1: Subtract 4 from both sides $$ \begin{align*} \frac{x}{3}+4-4&\leq4 - 4\ \frac{x}{3}&\leq0 \end{align*} $$ ## Step2: Multiply both sides by 3 $$ \begin{align*} x&\leq0\times3\ x&\leq0 \end{align*} $$ # Answer: $x\leq0$ 26. # Explanation: ## Step1: Subtract 3 from both sides $$ \begin{align*} 7m+3-3&>-81 - 3\ 7m&>-84 \end{align*} $$ ## Step2: Divide both sides by 7 $$ \begin{align*} m&>\frac{-84}{7}\ m&>-12 \end{align*} $$ # Answer: $m>-12$ 27. # Explanation: ## Step1: Expand the inequality $$ \begin{align*} -2 + 8p&>-8(1 - p)\ -2+8p&>-8 + 8p \end{align*} $$ ## Step2: Subtract $8p$ from both sides $$ \begin{align*} -2&>-8 \end{align*} $$ Since $-2>-8$ is always true, the solution is all real numbers. # Answer: All real numbers 28. # Explanation: ## Step1: Expand the inequality $$ \begin{align*} -32+3b&>-4(-3b + 8)\ -32+3b&>12b-32 \end{align*} $$ ## Step2: Subtract $3b$ from both sides $$ \begin{align*} -32&>12b-3b-32\ -32&>9b-32 \end{align*} $$ ## Step3: Add 32 to both sides $$ \begin{align*} 0&>9b \end{align*} $$ ## Step4: Divide both sides by 9 $$ \begin{align*} b&<0 \end{align*} $$ # Answer: $b<0$ 29. # Explanation: ## Step1: Expand the inequality $$ \begin{align*} 4(x + 2)&\geq-7+x\ 4x+8&\geq-7+x \end{align*} $$ ## Step2: Subtract $x$ from both sides $$ \begin{align*} 4x-x+8&\geq-7\ 3x+8&\geq-7 \end{align*} $$ ## Step3: Subtract 8 from both sides $$ \begin{align*} 3x&\geq-7-8\ 3x&\geq-15 \end{align*} $$ ## Step4: Divide both sides by 3 $$ \begin{align*} x&\geq\frac{-15}{3}\ x&\geq-5 \end{align*} $$ # Answer: $x\geq-5$ 30. # Explanation: ## Step1: Expand the inequality $$ \begin{align*} 3(1 + 6m)+6&\geq35+5m\ 3+18m+6&\geq35+5m \end{align*} $$ ## Step2: Combine like - terms $$ \begin{align*} 18m + 9&\geq35+5m \end{align*} $$ ## Step3: Subtract $5m$ from both sides $$ \begin{align*} 18m-5m+9&\geq35\ 13m+9&\geq35 \end{align*} $$ ## Step4: Subtract 9 from both sides $$ \begin{align*} 13m&\geq35 - 9\ 13m&\geq26 \end{align*} $$ ## Step5: Divide both sides by 13 $$ \begin{align*} m&\geq\frac{26}{13}\ m&\geq2 \end{align*} $$ # Answer: $m\geq2$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Expand the equation

Step2: Combine like - terms

Step3: Add \(5m\) to both sides

Step4: Add 19 to both sides

Step5: Solve for \(m\)

Step1: Expand the equation

Step2: Combine like - terms

Step3: Add \(14m\) to both sides

Step4: Subtract 24 from both sides

Step5: Solve for \(m\)

Step1: Expand the equation

Step2: Add \(6m\) to both sides

Step3: Add 3 to both sides

Step4: Solve for \(m\)

Answer: