3.01 Identifying and writing equations
What is an equation?
Determine whether each of the following is an expression or an equation:
4 p + 2 q - 10
5 r - 15 = 0
5 k = 15
x + 2
5 y - 8 \left(y - 9\right) = 6
7 x - 8 \left(x + 9\right)
u + v = 1
-2d + 4e - \left( 5f + 3 \right)
Write an equation for each of the following sentences:
y is equal to six.
n minus one equals three.
n plus eight equals fifteen.
The sum of y and two is equal to three.
a is the difference of b and seven, divided by two.
Five times m is equal to double the difference of b and ten.
x is equal to three groups of the sum of a and b.
q is added to p, and the result is one less than triple r.
For each of the following sentences:
Write an equation.
Find the value of n.
The sum of n and two gives eleven.
n is added to twenty to give forty five.
The difference of n and nine gives six.
n is subtracted from twelve to give four.
n multiplied by two gives six.
n is divided by three to give five.
Four multiplied by n gives twelve.
n is divided by two to give five.
Which of the following is the solution to the equation x-10 = 30?
Consider the equation x + 25 = 35.
Find the value of the left-hand side of the equation when x = 21.
Now, determine whether x = 21 is the solution of x + 25 = 35.
Consider the equation x - 48 = 96.
Find the value of the left-hand side of the equation when x = 144.
Now, determine whether x = 144 is the solution of x - 48 = 96.
Consider the equation 44 - n = 34.
Determine whether n = 10 is the solution of 44 - n = 34. Explain your answer.
Consider the equation 8 b = 63.
Determine whether b = 8 is the solution of 8 b = 63. Explain your answer.
Consider the equation 8 \div v = 4.
Determine whether v = 4 is the solution of 8 \div v = 4. Explain your answer.
Find the value of the variable that will make the following equations true:
Roxanne has been out picking 40 flowers to put in 5 different vases. If she puts p flowers in each vase, write an equation involving p.
Consider the shape in the diagram :
If A represents the total area of the shape, rewrite the following sentence as an equation:
"The total area of the shape is equal to the product of a and b, added to the product of b and c".
