Which of the following values for b makes the inequality −32.5−6b≥48.5 true?(1 point) Responses −13.5 negative 13.5 −12 negative 12 −13 negative 13 −12.5
To solve the inequality −32.5−6b≥48.5, we need to isolate the variable b.
First, let's subtract -32.5 from both sides of the inequality:
-32.5 - 32.5 - 6b ≥ 48.5 - 32.5
-6b ≥ 16
Next, divide both sides of the inequality by -6 (remember to flip the inequality sign since we are dividing by a negative number):
-6b/(-6) ≤ 16/(-6)
b ≤ -16/6
b ≤ -8/3
Therefore, the value for b that makes the inequality true is any value less than or equal to -8/3.
Among the given responses, -12.5 satisfies this condition, so the correct answer is -12.5.
Which of the following equations has the solution set {−3} ?(1 point) Responses 4x−8=−4 4 x minus 8 equals negative 4 4x+8=−4 4 x plus 8 equals negative 4 4x−8=4 4 x minus 8 equals 4 4x+8=4
To find the equation that has the solution set {−3}, we need to substitute -3 into each of the given equations and see which one satisfies the equation.
Let's substitute -3 into each equation:
1) 4x - 8 = -4:
4(-3) - 8 = -4
-12 - 8 = -4
-20 ≠ -4
2) 4x + 8 = -4:
4(-3) + 8 = -4
-12 + 8 = -4
-4 ≠ -4
3) 4x - 8 = 4:
4(-3) - 8 = 4
-12 - 8 = 4
-20 ≠ 4
4) 4x + 8 = 4:
4(-3) + 8 = 4
-12 + 8 = 4
-4 ≠ 4
None of the given equations give a solution of -3. Therefore, none of the provided equations has the solution set {−3}.
Which set expresses the solution to the compound inequality −2≤2x+13−4<1 ?(1 point) Responses {x:−32≤x<1} left brace x colon Start Fraction negative 3 over 2 End Fraction less-than-or-equal-to x less than 1 right brace {x:52≤x<7} left brace x colon Start Fraction 5 over 2 End Fraction less-than-or-equal-to x less than 7 right brace {x:3≤x<7} left brace x colon 3 less-than-or-equal-to x less than 7 right brace {x:52≤x<1}
To find the solution to the compound inequality −2≤2x+13−4<1, we need to solve both inequalities separately and then find the intersection of the solution sets.
Let's solve the left inequality: -2 ≤ 2x + 13 - 4.
-2 ≤ 2x + 9
Subtract 9 from both sides:
-11 ≤ 2x
Now, let's solve the right inequality: 2x + 13 - 4 < 1.
2x + 9 < 1
Subtract 9 from both sides:
2x < -8
Divide by 2 (since the coefficient of x is 2 and we want to isolate x):
x < -4
So the solution to the compound inequality is -11 ≤ 2x < -4.
Among the given responses, the set that expresses this solution is: {x:−32≤x<1}
To find the values of b that make the inequality true, we need to solve the inequality. Let's break it down step by step:
-32.5 - 6b ≥ 48.5
First, let's isolate the variable b. We can do this by adding 32.5 to both sides of the inequality:
-32.5 + 32.5 - 6b ≥ 48.5 + 32.5
Simplifying, we get:
-6b ≥ 81
Next, we divide both sides of the inequality by -6, remembering to reverse the direction of the inequality since we are dividing by a negative number:
(-6b)/(-6) ≤ 81/(-6)
Simplifying further, we have:
b ≤ -13.5
Now, we can determine which value for b satisfies the inequality. Looking at the given responses, we can see that -13.5 is among the options. Therefore, the answer is:
b ≤ -13.5
Hence, the correct response is: −13.5