To solve the following equation, what number should you divide both sides by? - 3 x = 12
Solve the following equations:
9 x - 45 = 4 x
- x - 7 = 7
6 x - 20 = x
2 x + 5 = x
5 x - 12 = x - 24
4 x + 24 = x - 9
9 p - 6 = 3 p + 24
8 x - 11 = 4 x
- 64 - 9 x = - 24 - x
36 - 2 k = 6 k + 20
3 \left(x - 10\right) = x
2 \left(x - 2\right) = x - 4
3 x + 2 \left( 3 x + 1\right) = 11
x - 2 \left(x + 3\right) = -1
3 x = - 13 - 4 \left( 2 x + 5\right)
2 \left( 2 x + 5\right) = 3 \left(x + 5\right)
4 \left(x + 35\right) - 3 \left( - x + 28\right) = - 7
9 \left(x - 9\right) - \left(x + 54\right) = 63 - \left(x - 63\right)
For the following word problems, construct an equation and solve it to find the value of x:
The product of 5 and the sum of x and 7 equals 50.
The difference of 5 from x muliplied by 3 is equal to - 15.
Let E represent an even integer.
If E is the smallest of three consecutive even integers, write an expression for:
The second even integer.
The third even integer.
Write an expression for the sum of the first and third consecutive even integers.
The sum of four consecutive odd numbers is 64. Let x be the smallest of the numbers.
Form an equation and solve it for x.
Find the four consecutive odd numbers.
Three consecutive integers are such that the sum of the first and twice the second, is 12 more than twice the third. Let x be the smallest of the numbers.
Form an equation and solve it for x.
Find the three consecutive integers.
The perimeter of the following triangle is 189\text{ cm}:
Write the perimeter in terms of x.
Solve for the value of x.
If the perimeter of the following triangle is 263\text{ cm}, form an equation and solve it for x.
The rectangle in the diagram provided has a perimeter of 212 + 14 x centimetres.
Find the value of x.
Consider the following quadrilateral with a perimeter of 315\text{ cm}:
Write an expression for the perimeter in terms of x.
Find the value of x.
Consider the complementary angles in the following diagram:
Form an equation and solve it for x.
Find the size of the angle marked by 4 x.
Consider the two angles given in the diagram:
Calculate the size of one of the angles.
Consider the following triangle:
Using an equation, find the value of x.
Find the size of the smallest angle in the triangle.
The cost, C, in dollars of sending x text messages is modelled by C = 0.1 \left(x - 400\right) + 8, where x \geq 400. Find the number of text messages x that have been sent if the total cost is \$20.70.
The relationship between F degrees Fahrenheit and C degrees Celsius is F = 1.8 C + 32.
Find the temperature in degrees Celsius, C, that is equivalent to 51.8 degrees Fahrenheit.
Kate and Isabelle do some fundraising for their sporting team. Together they raised \$600. Isabelle raised \$p and Kate raised \$272 more than Isabelle.
Write an equation in terms of p that represents the relationship between the different amounts and solve for p.
Calculate how much money Kate raised.
A Payroll Officer has been told to distribute a bonus to the employees of a company worth 14\% of the company’s net income. Since the bonus is an expense to the company, it must be subtracted from the income to determine the net income. If the company has an income of \$120\,000 before the bonus, then the Payroll Officer must solve the following equation to find the bonus B:
B = 0.14 \left(120\,000 - B\right)
Solve the equation to find B, correct to two decimal places.
One side of a parallelogram is 4\text{ cm} shorter than an adjacent side. Let x\text{ cm} be the length of the shorter side and y\text{ cm} be the length of the adjacent side to x. The perimeter of this parallelogram is 12\text{ cm}.
Express x in terms of y.
Write an equation in terms of y.
Solve the equation for y.
Find x, the length of the shorter side.
Vanessa is cutting out a rectangular board to construct a bookshelf. The board is to have a perimeter of 48 centimetres, and its length is to be 3 centimetres shorter than double the width. Let x be the width of the board.
Write an expression for the length of the board in terms of x.
Solve for x, the width of the board.
Hence, find the length of the board.
To solve the equation \dfrac{x}{4} = 8, you would first need to multiply both sides by what number?
Solve the following equations:
\dfrac{9}{n} = \dfrac{3}{4}
\dfrac{14 k - 76}{2} - 2 = 2 k
\dfrac{n}{45} = \dfrac{2}{15}
\dfrac{1}{n - 2} = \dfrac{1}{9}
\dfrac{1}{8} \left(2 - 6 x\right) = \dfrac{1}{3} \left(8 + 5 x\right)
\dfrac{4 n}{3} + \dfrac{1}{2} = \dfrac{6 n - 5}{6}
\dfrac{1}{4 m + 4} + 2 = - \dfrac{1}{5}
When a number is added to both the numerator and denominator of \dfrac{1}{5}, the result is \dfrac{3}{7}.
If n represents the number, find the value of n.
Consider the equation \dfrac{x - 1}{x - 1} = 5.
Yvonne is trying to solve the equation. Her next step is x - 1 = 5 \left(x - 1\right).
For what values of x is this a valid step of working?
How many solutions does the equation \dfrac{x - 1}{x - 1} = 5 have?
The quotient of a number, x, and 10, minus 7, equals \dfrac{6}{5}. Write an equation and solve for x.
One quarter of a number, x, is equal to triple that number less 22. Solve the equation for x.
A construction company has spent \$22\,500\,000 to develop new cranes, and wants to limit the cost of development and production of each crane to \$6000.
Given that the production cost of each crane is \$3000, the cost for development and production of x cranes is given by 3000 x + 22\,500\,000 dollars, and so the cost of each crane is \dfrac{3000 x + 22\,500\,000}{x} which we want to equal \$6000. Hence, find the number of cranes that must be sold.
The sum of the reciprocals of two integers with a difference of 7 is equal to 11 times the reciprocal of their product. Find the integers.
Solve \dfrac{a x}{b} + \dfrac{m x}{n} = 6 for x, expressing the solution in terms of a, b, m and n.