Combining like terms
distributive property
one-step equation
two-step equation
multi-step equation
100
Which of these are like terms in the following expression:3x + 7 - 9x + 24y + 2x2
1.7, 24y
2.3x, 9x
3.3x, -9x
4.3x, -9x, 2x2
3.3x, -9x
100
The sum of two numbers is s. The product of the same two numbers is p. If the two numbers are each increased by one, the new product is q. Find q−p in terms of s.
Possible Answers:
1.2s+1
2.s+2
3.s2
4.s−1
5.s+1
5.s+1
Let the two numbers be x and y.
x + y = s
xy = p
(x + 1)(y + 1) = q
Expand the last equation:
xy + x + y + 1 = q
Note that both of the first two equations can be substituted into this new equation:
p + s + 1 = q
Solve this equation for q – p by subtracting p from both sides:
s + 1 = q – p
100
Find the variable.
13 + q = 56
1.43
2.40
3..q
4.42
1.43
100
1. 3c + 5 = 23
1.c = 3
2.c = 6
3.c = 7
4.c = 18
2.c=6
200
Simplify by combining like terms:
5a + 2b - 3a + 4
1.8a + 2b + 4
2.2a + 2b + 4
3.8ab
4.4ab + 4
2.2a + 2b + 4
200
Expand the expression:
Possible Answers:
1.
2.
3.
4.
5.
5.
Explanation:
When using FOIL, multiply the first, outside, inside, then last expressions; then combine like terms.
200
13. Simplify by combining like terms:
7v + 2 + 12 + 2v
1.23
2.23v
3.9 + 14v
4.9v + 14
4.9v + 14
200
4x + 7 = 23
1.x = 16
2.x = 4
3.x = 9
4.x = 12
2.x = 4
200
2. How to solve a multi-step equation?
1. First, you get the variables on the same side of the equal sign. Add the number that you have to both sides so that the variable remains on one side only. Now isolate the variable by subtracting by another number from both sides. Multiply both sides and then divide
2. First, take the log of both sides, and solve for the variable.
1. First, you get the variables on the same side of the equal sign. Add the number that you have to both sides so that the variable remains on one side only. Now isolate the variable by subtracting by another number from both sides. Multiply both sides and then divide
300
Simplify by combining like terms:
4x2 - 3x + 11 -2x
1.4x2 - 5x + 11
2.11x + 11
3.16x2 - 5x + 11
4.10x2
1.4x2 - 5x + 11
300
Expand the following expression:
(4x+2)(x2−2)
Possible Answers:
1.4x3+2x2+8x+4
2.4x3+4x−4
3.x3+2x2−8x−4
4.4x3−4
5.4x3+2x2−8x−4
Correct answer:
4x3+2x2−8x−4
Explanation:
(4x+2)(x2−2)=(4x×x2)+(4x×−2)+(2×x2)+(2×−2)
Which becomes
4x3−8x+2x2−4
Or, written better
4x3+2x2−8x−4
300
14. Simplify the following expression:
3 + 5x + 8 - 2x
1.-3x2 - 11
2.3x2 + 11
3.11 - 3x
4.11 + 3x
4.11 + 3x
300
What is the first step to solve this equation:
11 - 3x = 44
1.Add 3 to both sides
2.Subtract 11 from both sides
3.Add 11 to both sides
4.Divide 3 on both sides.
2.Subtract 11 from both sides
300
3. How to multiply multi-step equations?
1.Divided a number into a whole number
2.Multiply by the reciprocal of the coefficient on the variable term to solve for the variable
2.Multiply by the reciprocal of the coefficient on the variable term to solve for the variable
400
-r - 10r
a.11r
b.-11r
c.9r
d.-11
b.-11r
400
Simplify the expression.
(2x2−3x)(2y+a)
Possible Answers:
1.None of the other answers
2.−6x3+2ay
3.−2axy
4.2x2y−2ax2−3xy−3ax
5.4x2y+2ax2−6xy−3ax
Correct answer:
5.4x2y+2ax2−6xy−3ax
Explanation:
Solve by applying FOIL:
First: 2x2 * 2y = 4x2y
Outer: 2x2 * a = 2ax2
Inner: –3x * 2y = –6xy
Last: –3x * a = –3ax
Add them together: 4x2y + 2ax2 – 6xy – 3ax
There are no common terms, so we are done.
400
1467 + x = 1653
1. x = 3120
2. x = 186
3. x = 286
4. x = 3020
2. x = 186
400
5. In the equation 4y +-9 =-36
y = -4
1.True
2. Francine
3.False
3.False
400
5. How to add multi-step equations?
1. Write down the numbers, one under the other, with the decimal points lined up.
2.Simplify the fraction
3. You have to add the number that you have on both sides so that the variable remains on one side only.
3. You have to add the number that you have on both sides so that the variable remains on one side only.
500
Simplify the following expression:
-10x + 15 - 3x + 2
a.13x2 + 17
b.-13x2 + 13
c.-13x + 17
d.-7x + 17
c.-13x + 17
500
(6x−2)(3x+5)=ax2+dx+k
Given the equation above, what is the value of a−d+k?
Possible Answers:
1.−10
2.−16
3.2
4.9
5.24
2.−16
Explanation:
(6x−2)(3x+5)=ax2+dx+k
Use FOIL to expand the left side of the equation.
(6x−2)(3x+5)=18x2+30x−6x−10=18x2+24x−10
18x2+24x−10=ax2+dx+k
From this equation, we can solve for a, d, and k.
18x2=ax2→a=18
24x=dx→d=24
−10=k
Plug these values into a−d+k to solve.
a−d+k=(18)−(24)+(−10)=−16
500
What is the inverse operation needed to solve for p?
765 = p - 254
1.subtraction
2.addition
3.multiplication
4.division
2.addition
500
What is the first step to solve this equation:
11 - 3x = 44
1. Add 3 to both sides
2.Subtract 11 from both sides
3. Add 11 to both sides
4.Divide 3 on both sides.
2.Subtract 11 from both sides
500
10. 3n+5=6
A.1/5
B.1/2
C.1/3
D.1/4
C.1/3