1. solve the inequality -3/4x + 6 > -3.
x > -2
x < -2
x > 12
x < 12
2.
what is the solution to the inequality -4x < 8?
x < -24
x > -24
x < -2
x > -2
3.
the total cost for four people to bowl one game is $21. each person paid $1.50 to rent their shoes, in addition to the cost of the game, c. which of the following equations could be used to find the value of c?
4(c + 1.5) = 21
4c + 1.5 = 21
4(c + 6) = 21
4c - 6 = 21
4.
what is the solution set of -11 > 1 + a?
a < -12
a > -12
a < -10
a > -10
5.
which of the following inequalities is equivalent to 1 ≥ x?
x ≥ 1
x ≥ -1
x ≤ -1
x ≤ 1
6.
translate the following sentence to an inequality.
a number is no less than seven.
n > 7
n < 7
n ≥ 7
n ≤ 7
7.
which of the following mathematical properties is described by the statement, “whatever is done on one side of the equation must also be done on the other side of the equation”?
communitive property
property of equality
associative property
identity property of addition
8.
what steps would you follow in order to solve the equation?
w/8 -4 =20
add 4 on each side and divide by 8
subtract 4 on each side and multiply by 8
add 4 on each side and multiply by 8
subtract 4 on each side and divide by 8
9.
the speed limit on a highway is 75 miles per hour. which of the following inequalities represents this situation?
x ≤ 75
x ≥ 75
x < 75
x > 75
10.
how would you graph the solution to x/3 ≤ -2?
draw a closed circle on -6 and shade to the right.
draw a closed circle on -6 and shade to the left.
draw an open circle on -6 and shade to the right.
draw an open circle on -6 and shade to the left.
11.
translate the following sentence to an equation.
the sum of five times a number and four is equal to negative eleven.
5n + 4 = -11
5n - 4 = -11
4n + 5 = -11
4n - 5 = -11
12.
what steps should be followed to solve the inequality -4x < 8.
multiply by -4 on each side and keep the sign.
divide by -4 on each side and flip the sign.
multiply by -4 on each side and flip the sign.
divide by -4 on each side and keep the sign.
13.
the sum of five times a number and four is equal to negative eleven. what is the number?
-2
-3
-4
-5
14.
which of the following symbols indicates that a value is included in a solution set.
=
≠
○
●

part 1)

part 2)

part 3)

part 4)

part 5)

part 6)

part 7) property of equality

part 8)   add on each side and multiply by

part 9)

part 10) draw a closed circle on and shade to the left

part 11)

part 12) divide by on each side and flip the sign

part 13)

part 14) the closed circle ●

step-by-step explanation:

part 1) we have

multiply by both sides

subtract both sides

> multiply by  

part 2) we have

divide by both sides

  > multiply by

part 3)

let

> cost of the game for each person

> cost of the rent of shoes per person

we know that

  > equation a

substitute the value of s in the equation a

part 4) we have

subtract both sides

>

part 5) we have

> equivalent to

part 6) we have

a number is no less than seven

if the number is no less than seven

then

the number is greater than seven

let

> the number

part 7) we know that

the property of equality establishes that if what is done on one side of the equation is also done on the other side of the equation, then equality remains true

part 8) we have

step 1

adds both sides  

step 2

multiply by both sides          

therefore

add on each side and multiply by

part 9) we have

the speed limit on a highway is miles per hour

that means

the speed must be less than or equal to miles per hour

so

let

> the speed in miles per hour

the inequality that represent this situation is

part 10) we have

multiply by both sides

the solution is the > (-∞,-6]

the number is included in the solution set

therefore

draw a closed circle on and shade to the left

part 11) we have

the sum of five times a number and four is equal to negative eleven

let

> the number

we know that

the sum of five times a number and four >

equal to negative eleven >

the complete equation that represent this situation is

part 12) we have

divide by on each side and flip the sign

part 13) we have

the sum of five times a number and four is equal to negative eleven. what is the number?

let

> the number

we know that

the equation that represent the situation is

subtract on each side

divide by on each side

part 14) we know that

the symbol that indicate that a value is included in a solution set is

the closed circle ●

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

slope is 35 and 20 miles is the y-intercept.

step-by-step explanation: