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Equations from Word Problems
Checking solutions
Problems involving angles
Solving with Equations
Number of Solutions
100
The sum of two consecutive numbers is -27. Write an equation.
x + x + 1 = -27 OR 2x + 1 = -27
100
Is x = 1 a solution to the equation 8 + 2x = 40?
No. 8 + 2(1) = 10, not 40.
100
Two angles are complimentary. One of the angles is 35 degrees, what is the other angle?
55 degrees.
100
r + 11 + 8r = 29
r = 2
100
How many solutions would the equation 4x + 5=4x + 5 have.
Infinite solutions
200
The sum of 13 and twice a number is seven less than six times a number.
13 + 2x = 6x - 7
200
Is x = -1 a solution to the equation 8(2x+9) =56
Yes. 8(2(-1)+9) 8(7) = 56
200
Two angles are supplementary, one of the angles is 71 degrees, what is the other angle?
109 degrees.
200
a - 2 + 3 = -2
a = -3
200
How many solutions would 4x + 5=2x - 5 have?
One solution.
300
Eight times the result of subtracting 3 from a number is equal to the number increased by 25.
8(x-3) = x + 25
300
Is x = 5 a solution to the equation 11 (x+10) = 132.
No. 11(5 + 10) does not equal 132.
300
The measure of one angle is 13 less than five times the measure of another angle. The sum of the measures of the angles is 140 degrees. Come up with an equation, solve for x, and determine the angle measures.
x + (5x -13) = 140 6x - 13 = 140 x = 23.5 angle 1: 23.5 angle 2: 114.5
300
8=8v - 4(v+8)
v=10
300
How many solutions would -7x + 4 = -7x - 4 have?
No solutions.
400
Three consecutive odd integers have a sum of 3. What are the numbers.
x + (x + 2) + (x + 4) = 3
400
Is x = 2 a solution to the equation: 16x + 21 = 28x + 9
No. 16(2) + 21 = 28(2) + 9 32 + 21 = 56 + 9 53 = 65 FALSE.
400
Two angles are complementary> One angle is one less than six times the measure of another. Find the measure of each angle.
x + 6x - 1 = 90 7x -1 = 90 x= 13. Angle 1: 13. Angle 2: 77.
400
10(1+3b)=-20
b=-1
400
How many solutions would 5(x+4) = 5x + 4 have?
No solutions.
500
The width of a rectangle is 7 less than twice the length. If the perimeter of the rectangle is 45 inches, write an equation to solve for x.
6x - 14 = 45
500
Is x = -31 a solution to the equation 3(2x-14) + x = 15 - (-9x - 5)
Yes. 3(2(-31) - 14) + -31 = 15 - (-9(-31) - 5) 3(-62 - 14) + -31 = 15 -(279 - 5) 3(-76) + -31 = 15 - (274) -228 + -31 = -259 -259 = -259
500
A triangle has the following angles. The measure of the first angle is four more than seven times a number. The measure of the second angle is seven times a number. The measure of the third angle is twice as large as the first. What is the measure of each angle in degrees?
(7x + 4)+ (7x) + 2(7x+4) = 180 14x + 4 + 14x + 4 = 180 28x + 8 = 180 x = 6 Angle 1: 46 degrees. Angle 2: 42 degrees. Angle 3: 92 degrees.
500
8(1+5x) + 5 = 13 + 5x
x=0
500
How many solutions would 2(x+3) = 4x - 15 + 3x have?
One solution.