Which of the following values for x makes the inequality √4x+1 ≤ 5.83 true?(1 point)
10, 8, 9, 9.5
To solve the inequality √4x+1 ≤ 5.83, we can start by subtracting 1 from both sides:
√4x ≤ 4.83
Next, we can square both sides to eliminate the square root:
(√4x)^2 ≤ (4.83)^2
4x ≤ 23.3489
Now, we can divide both sides by 4 to isolate x:
x ≤ 5.837225
Among the given options, the only value of x that satisfies the inequality is 9, since 9 is less than 5.837225.
To find which values of x make the inequality √4x+1 ≤ 5.83 true, we need to solve the inequality. Here are the steps:
1. Start with the given inequality: √4x+1 ≤ 5.83.
2. Subtract 1 from both sides to isolate the square root term: √4x ≤ 4.83.
3. Square both sides of the inequality to eliminate the square root: 4x ≤ (4.83)^2.
4. Simplify the right side: 4x ≤ 23.3489.
5. Divide both sides by 4 to solve for x: x ≤ 5.837225.
Now, we need to determine which of the given values for x satisfy the inequality.
- If x = 10: 10 is not less than or equal to 5.837225. Therefore, 10 does not make the inequality true.
- If x = 8: 8 is not less than or equal to 5.837225. Therefore, 8 does not make the inequality true.
- If x = 9: 9 is not less than or equal to 5.837225. Therefore, 9 does not make the inequality true.
- If x = 9.5: 9.5 is less than or equal to 5.837225. Therefore, 9.5 makes the inequality true.
So, the value for x that makes the inequality true is 9.5.
To determine which values of x make the inequality √4x+1 ≤ 5.83 true, we can solve the inequality step by step.
Given inequality: √4x+1 ≤ 5.83
Step 1: Subtract 1 from both sides of the inequality:
√4x ≤ 5.83 - 1
√4x ≤ 4.83
Step 2: Square both sides of the inequality:
(√4x)^2 ≤ (4.83)^2
4x ≤ 23.3489
Step 3: Divide both sides of the inequality by 4:
4x/4 ≤ 23.3489/4
x ≤ 5.837225
Therefore, the values of x that make the inequality true are any values less than or equal to 5.837225.
Now, let's check which of the given options satisfy this condition:
- Option 10: Since 10 is greater than 5.837225, it does not satisfy the inequality.
- Option 8: Since 8 is greater than 5.837225, it does not satisfy the inequality.
- Option 9: Since 9 is greater than 5.837225, it does not satisfy the inequality.
- Option 9.5: Since 9.5 is greater than 5.837225, it does not satisfy the inequality.
Therefore, none of the given values for x satisfy the inequality √4x+1 ≤ 5.83.