Consider the following expressions: 6−14⋅28−214 _______ 34+4⋅2−11 . Which operator can be inserted to make the statement true? (1 point) Responses = equals > greater than < less than ≥ greater-than-or-equal-to
To make the statement true, we need to determine the correct operator to insert. Comparing the two expressions, we see that 6 - 14 ⋅ 28 - 214 is being compared to 34 + 4 ⋅ 2 - 11.
The value of 6 - 14 ⋅ 28 - 214 is -392, and the value of 34 + 4 ⋅ 2 - 11 is 37.
Since -392 is less than 37, the correct operator to insert is < (less than).
Which of the following values for b makes the inequality −32.5−6b≥48.5 true?(1 point) Responses −13 negative 13 −12 negative 12 −13.5 negative 13.5 −12.5 negative 12.5
To solve the inequality -32.5 - 6b ≥ 48.5, we need to isolate the variable b.
First, let's add 32.5 to both sides of the inequality:
-32.5 + 32.5 - 6b ≥ 48.5 + 32.5
Simplifying:
-6b ≥ 81
Next, we divide both sides of the inequality by -6. It's important to remember that when we divide or multiply both sides of the inequality by a negative number, we must reverse the inequality sign.
-6b/(-6) ≤ 81/(-6)
Simplifying:
b ≤ -13.5
The inequality is true for any value of b that is less than or equal to -13.5.
Therefore, the correct response is: -13.5 negative 13.5
Which of the following equations has the solution set {−3} ?(1 point) Responses 4x+8=−4 4 x plus 8 equals negative 4 4x−8=4 4 x minus 8 equals 4 4x−8=−4 4 x minus 8 equals negative 4 4x+8=4 4 x plus 8 equals 4
To find which equation has the solution set {-3}, we can substitute -3 for the variable x in each equation and see which one satisfies the equation.
1) 4x+8=-4
Substituting -3 for x:
4(-3) + 8 = -4
-12 + 8 = -4
-4 = -4
This equation is not satisfied by the solution -3, so it is not the correct equation.
2) 4x-8=4
Substituting -3 for x:
4(-3) - 8 = 4
-12 - 8 = 4
-20 = 4
This equation is also not satisfied by the solution -3, so it is not the correct equation.
3) 4x-8=-4
Substituting -3 for x:
4(-3) - 8 = -4
-12 - 8 = -4
-20 = -4
This equation is not satisfied by the solution -3, so it is not the correct equation.
4) 4x+8=4
Substituting -3 for x:
4(-3) + 8 = 4
-12 + 8 = 4
-4 = 4
This equation is not satisfied by the solution -3, so it is not the correct equation.
Based on the above analysis, 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<1} left brace x colon Start Fraction 5 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
To solve the compound inequality -2 ≤ 2x + 13 - 4 < 1, we need to isolate the variable x.
First, let's simplify the expression:
-2 ≤ 2x + 13 - 4 < 1
Combine like terms:
-2 ≤ 2x + 9 < 1
Next, let's isolate 2x:
-2 - 9 ≤ 2x < 1 - 9
Simplifying:
-11 ≤ 2x < -8
Now, we can divide all three parts of the inequality by 2 (since we want to isolate x):
-11/2 ≤ 2x/2 < -8/2
Simplifying:
-11/2 ≤ x < -4
Therefore, the correct response is: {x: -11/2 ≤ x < -4} or in decimal form, {x: -5.5 ≤ x < -4}.
What property of equality is displayed in step 3 in the solving of 9m+4−7m=5m+73 ? Step 1: 9m+4−7m=5m+73 9m−7m+4=5m+73 Step 2: 2m+4=5m+73 3(2m+4)=(5m+73)3 Step 3: 6m+12=5m+7 6m+12−12=5m+7−12 Step 4: 6m=5m−5 6m−5m=5m−5m−5 m=−5 (1 point) Responses Addition Property of Equality Addition Property of Equality Multiplication Property of Equality Multiplication Property of Equality Division Property of Equality Division Property of Equality Subtraction Property of Equality Subtraction Property of Equality
The property of equality displayed in Step 3 of the solving process is the Subtraction Property of Equality.
In Step 2, we have 6m + 12 = 5m + 7. To isolate the variable m, we subtract 12 from both sides of the equation in Step 3.
6m + 12 - 12 = 5m + 7 - 12
Simplifying:
6m = 5m - 5
So, the Subtraction Property of Equality is used in Step 3.