1. Compare the quantity in Column A with the quantity in Column B.
Column A
slope of y = 2x +2
Column B
slope of 2y = 3x +9
Answer-Column A is greater
2. |x-4| < 3
Answer- 1< x < 7
3. Solve for x in 3x + 4 =28
Answer-8
4. An algebraic ___________ has an equal sign.
It is either expression or equation.
5. Simplify .5(2.3 + 25) / 1.5 to the nearest tenth.
Answer- 9.1
1) agree
2) x-4<3 or 4-x<3
x <-1 or -x <3 which is x>-3
so I get -3<x<-1
3)agree, 8
4)equation has = sign
5) 27.3/3 = 9.1 exactly
For this question my answer's are:
|x - 4| <3
a. -7< x <-1
b. 1< x <7
c. 1> x >7
d. -7> x >-1
It does not have the answer you gave.
|x-4| < 3
x-4 < 3 and -x + 4 < 3
x < 7 and x > 1
so
1 < x < 7
(looks like you have a - in front of 1
1. To compare the quantities in Column A and Column B, we need to compare the slopes of the given equations.
For Column A, the slope of the equation y = 2x + 2 is 2.
For Column B, the slope of the equation 2y = 3x + 9 can be found by rearranging the equation to solve for y:
2y = 3x + 9
Dividing both sides by 2:
y = (3/2)x + 4.5
The slope of the equation in Column B is (3/2), which is less than 2. Therefore, the answer is that Column A is greater.
2. The inequality |x - 4| < 3 can be read as "The absolute value of (x - 4) is less than 3." To solve this inequality, we'll split it into two cases:
Case 1: x - 4 > 0
In this case, the absolute value is not needed:
x - 4 < 3
Adding 4 to both sides:
x < 7
Case 2: x - 4 < 0
In this case, we need to reverse the inequality when removing the absolute value:
-(x - 4) < 3
Expanding the negative sign:
-x + 4 < 3
Subtracting 4 from both sides:
-x < -1
Multiplying both sides by -1 (and reversing the inequality because we're multiplying by a negative):
x > 1
Combining both cases, we get 1 < x < 7 as the solution.
3. To solve the equation 3x + 4 = 28, we want to isolate the variable x.
Begin by subtracting 4 from both sides of the equation:
3x = 28 - 4
3x = 24
Then, divide both sides by 3 to solve for x:
x = 24/3
x = 8
So, the solution to the equation is x = 8.
4. An algebraic term that has an equal sign is called either an expression or an equation. Both expressions and equations consist of variables, constants, and mathematical operations. However, an equation is a statement that states two expressions are equal, while an expression is a mathematical phrase with no equal sign.
5. To simplify the expression .5(2.3 + 25) / 1.5 to the nearest tenth, follow the order of operations (PEMDAS/BODMAS):
First, simplify the parentheses:
2.3 + 25 = 27.3
Then, perform the multiplication:
.5 * 27.3 = 13.65
Finally, divide by 1.5:
13.65 / 1.5 = 9.1
Therefore, the simplified expression to the nearest tenth is 9.1.