Solve the following equations:
5 x - 8 = 2
- x - 7 = 7
\dfrac {c - 4}{4} = 7
5 \left(y + 1\right) = 25
- \dfrac {6 x}{5} + 5 = 35
\dfrac {11 x + 22}{8} = 33
\dfrac {3 x - 15}{5} = 9
6 x - 20 = x
9 x - 45 = 4 x
5 x + 2 = 3 x + 22
9 p - 6 = 3 p + 24
3 \left(x + 1\right) + 2 = -1
- 2 \left(x + 2\right) - 6 = - 20
3 \left(x + 6\right) + 3 \left(x + 24\right) = 12
2 \left( 2 x + 5\right) = 3 \left(x + 5\right)
\dfrac {1}{8} \left(2 - 6 x\right) = \dfrac {1}{3} \left(8 + 5 x\right)
- n - \dfrac {7}{8} = 3
5 x - \dfrac {104}{5} = x
8 x - 11 = 4 x
5 \left( 2 x + 2\right) = - 3 \left( 4 x - 5\right) + 5 x
State whether we can immediately use cross multiplication to solve the following equations for x. Note: you do not need to solve the equations.
\dfrac {5 - x}{6} = \dfrac {2 + x}{7}
\dfrac {2}{3} - x = \dfrac {5 + x}{5}
Solve the following equations:
\dfrac {7 n - 10}{2} + 2 = 3 n
\dfrac {10 x - 46}{2} + 2 = 2 x
\dfrac {10 x - 26}{2} + 3 = 4 x
x + \dfrac {5 x-1}{4} = 1
x + \dfrac {4 x - 7}{2} = 9
\dfrac {8 p - 4}{4} = \dfrac {7 p + 3}{5}
\dfrac {8 x - 2}{3} = \dfrac {6 x - 3}{4}
\dfrac {6 y - 4}{4} = \dfrac {y - 3}{5}
\dfrac {9 x}{3} + \dfrac {9 x}{2} = - 5
\dfrac {2}{5 x - 5} = \dfrac {- 5}{2 x + 1}
\dfrac {2}{5 q - 3} = \dfrac {- 5}{2 q + 1}
\dfrac {4}{5 w - 3} = \dfrac {- 5}{4 w + 2}
\dfrac {5 x}{4} - 6 = \dfrac {3 x}{9}
\dfrac {3 x}{2} + 5 = \dfrac {2 x}{3}
\dfrac {2 x}{3} - 2 = \dfrac {5 x}{2} + 4
\dfrac {4 n}{3} + \dfrac {1}{2} = \dfrac {6 n - 5}{6}
\dfrac {4 m}{5} + \dfrac {1}{2} = \dfrac {4 m - 3}{10}
\dfrac {4 x}{3} + \dfrac {1}{4} = \dfrac {6 x - 7}{12}
\dfrac {x + 2}{2} + 3 = \dfrac {x + 3}{7}
\dfrac {y + 3}{3} + 2 = \dfrac {y + 5}{7}
If the perimeter of this triangle is 263\text{ cm}, find the value of x.
The following rectangle has a perimeter of 126 + 3 y centimetres.
Find the value of y.
The total flying time for two flights is 9 hours. The flight time for the first flight is half of the second.
Let f be the flight time of the second flight. Find the value of f.
What was the flight time of each flight?
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.
John and Uther do some fundraising for their sporting team. John raised \$m, and Uther raised \$71. Together they raised \$403. Find the value of m.
The product of 5 and the sum of x and 7 equals 50.
Consider the following quadrilateral with a perimeter of 315\text{ cm}:
Write an equation for the perimeter, in terms of x.
Find the value of x.
Let x be the smallest of three consecutive even integers.
Write an expression for:
The second integer
The third integer
Write an expression for the sum of the first and third consecutive even integers.
Find three consecutive even integers whose sum is 36.
Find four consecutive odd integers whose sum is 64.
Three consecutive integers are such that the sum of the first and twice the second is 12 more than twice the third. Find the three integers.
One quarter of a number is equal to triple that number less 22. Find the unknown number.
Consider the angles marked in the following diagram:
Find x, correct to two decimal places.
Find the size of the angle marked by 4 x, correct to two decimal places.
Vanessa is cutting out a rectangular board to construct a bookshelf. The board is to have a perimeter of 48 cm, and its length is to be 3 cm 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.
Write an equation for the perimeter of the board, in terms of x.
Solve for x, the width of the board.
Hence, state the length of the board.
Marge is looking at accommodation prices in Paris. One particular hotel charges \$184.70 for the first night, and then \$153.97 for every additional night. Marge has a budget of \$1108.52.
Let n represent the number of nights Marge can stay at the hotel. Write an equation in terms of n and solve it to determine how many nights she can afford to stay.
Valentina tries to guess how many people are at a concert, but she guesses 400 too many. Kenneth guesses 150 too few. The average of their guesses is 3625.
Let x be the exact number of people at the concert. Find the value of x.
To manufacture sofas, the manufacturer has a fixed cost of \$27\,600 plus a variable cost of \$170 per sofa. Find the number of sofas that need to be produced so that the average cost per sofa is \$290.