For each of the following equations, describe what must be done to both sides in order to solve the equation:
x - 4 = 6
Solve:
Consider the equation - \dfrac{q}{9} = 6.
Describe what must be done to make q the subject of the equation.
Hence, find q.
Solve:
3 x + 11 = 5
12 q + 8 = 26
4 s - 9 = 39
- 6 s + 5 = 47
6 t + 2 = - 22
Ryan attempted to solve the equation 9 \left( 4x - 6 \right) = 18. His working is shown below:
\begin{aligned} 9 \left( 4x - 6 \right) &= 18 \\ 4x - 6 &= 9 \\ 4x &= 15 \\x &= \dfrac{15}{4} \end{aligned}What was his mistake?
Solve the equation correctly.
Solve:
Explain what should be done to solve the equation 9 x = 7 + 8 x.
Solve:
7 x = x + 30
3 x = x - 18
7 x + 6 = 3 x + 22
6 x - 3 = 4 x + 7
5 x - 3 = - 4 x + 33
4 x - 9 = 5 x - 6
Solve:
5 \left( 2 x + 5\right) =2x + 13
6 \left( 3 x + 1\right) =4x + 20
4 \left( 3 x - 2\right) =6x + 16
2 \left(8 - 3 x\right) =10x - 20
3 x + 4 = 5 \left( 6 x + 5\right) + 60
Solve:
Solve:
Write an equation for each of the following statements, then solve it to find x:
When 4 is added to x, the result is 11.
When 8 is subtracted from 2x, the result is 6 more than x.
When triple the value of x+1 is added to 4, the result is 5 less than the value of 6x.
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.
A square has a side length of \, 4x + 5\text{ cm}. If the perimeter of the square is 44 \text{ cm}, find the value of x.
A rectangle has a width of \, 5x-3\text{ cm} and a height of \, 3x + 7\text{ cm}. If the perimeter of the rectangle is 42 \text{ cm}, find the value of x.
A number is multiplied by 5 and then 2 is added. Then the result is multiplied by 6. This is equal to 10 times the number minus 8.
Form an equation for this problem.
Solve the equation to find the number.
A rectangle with a height of 3x + 7 \text{ cm} and a width of 4x has the same perimeter as a square with side length 2x+9\text{ cm}.
Find the value of x.
A square with side length 4x - 11 \text{ cm} has the same perimeter as a square with side length 2x+9\text{ cm}.
Find the value of x.
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.
Solve for x, the width of the board.
Hence, state the length of the board.
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.