Question

Answer this please I really need you to do this

Answer 1

x ≥ 2

Explanation:

Given inequality:

`-(4(x+3))/(5) \leq 4x-12`

Values of x less than 2

Substitute two values where x < 2 into the inequality:

`\begin{aligned}x=1 \implies -(4(1+3))/(5) & \leq 4(1)-12\\\\ -(4(4))/(5) & \leq 4-12\\\\ -(16)/(5) & \leq -8 \quad \Rightarrow \textsf{Not a solution}\end{aligned}`

`\begin{aligned}x=0 \implies -(4(0+3))/(5) & \leq 4(0)-12\\\\ -(4(3))/(5) & \leq 0-12\\\\ -(12)/(5) & \leq -12 \quad \Rightarrow \textsf{Not a solution}\end{aligned}`

The values of x < 2 are not solutions to the inequality.

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Substitute the value of x = 2 into the inequality:

`\begin{aligned}x=0 \implies -(4(2+3))/(5) & \leq 4(2)-12\\\\ -(4(5))/(5) & \leq 8-12\\\\ -(20)/(5) & \leq -4\\\\ -4 & \leq -4 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}`

The value of x = 2 is a solution to the inequality.

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Values of x more than 2

Substitute two values where x > 2 into the inequality:

`\begin{aligned}x=3 \implies -(4(3+3))/(5) & \leq 4(3)-12\\\\ -(4(6))/(5) & \leq 12-12\\\\ -(24)/(5) & \leq 0 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}`

`\begin{aligned}x=4 \implies -(4(4+3))/(5) & \leq 4(4)-12\\\\ -(4(7))/(5) & \leq 16-12\\\\ -(28)/(5) & \leq 4 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}`

The values of x > 2 are solutions to the inequality.

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Therefore, the solution to the inequality appears to be x ≥ 2.

To check, solve the inequality:

`\begin{aligned} \implies -(4(x+3))/(5) &\leq 4x-12\\-4(x+3) &\leq 5(4x-12)\\-4x-12 &\leq 20x-60\\ -24x & \leq-48\\x & \geq 2\end{aligned}`

When graphing inequalities on a number line:

• < or > : open circle.
• ≤ or ≥ : closed circle.
• < or ≤ : shade to the left of the circle.
• > or ≥ : shade to the right of the circle.

To graph the solution to the inequality on number line, place a closed circle at x = 2 and shade to the right. (See attachment).