5.03 Distributing to solve
Use substitution to determine whether the given value of x is the solution to each equation:
x = 6 where 2 \left(x - 3\right) = - 8.
x = 8 where 7 \left(x - 6\right) = 14.
x = 8 where 3 \left(x - 6\right) = 6.
x = 8 where 9 = 7 \left(x - 7\right).
Solve the following equations by first expanding the brackets:
4 \left(x + 5\right) = 32
5 \left(x + 5\right) = 39
4 \left(x + 6\right) = - 60
12 \left(x + 5\right) = 168
3 \left(x - 4\right) = - 21
4 \left(x - 6\right) = - 5
5 \left( x - 4\right) = -15
12 \left(x - 6\right) = 12
5 \left( 2 x + 6\right) = 69
6 \left( 3 x + 5\right) = 192
9 \left( 3 x + 5\right) = 153
6 \left( 2 x - 6\right) = - 90
6 \left( 3 x - 5\right) = - 102
9 \left( 3 x - 5\right) = 63
- 6 \left( 4 x + 5\right) = - 143
- 6 \left( 3 x + 6\right) = 54
- 8 \left( 4 x + 5\right) = 120
- 6 \left( 2 x - 4\right) = 81
- 6 \left( 4 x - 5\right) = 174
- 8 \left( 2 x - 6\right) = - 16
Solve the following equations:
4 \left( 2 x + 5\right) + 4 = 48
6 \left( 4 x + 8\right) - 9 = 87
5 \left( 4 x + 5\right) + 3 x = 71
4 \left( 2 x - 6\right) - 3 x = 16
5 \left( 2 x + 5\right) + 4 x + 6 = 59
4 \left( 4 x - 6\right) - 3 x + 8 = 36
- 3 \left( 4 x + 7\right) + 3 x - 5 = - 8
- 4 \left( 4 x + 7\right) - 3 x + 5 = 15
- 3 \left( 4 x + 6\right) - 3 x - 7 = - 70
- 4 \left( 4 x + 6\right) + 3 x + 7 = - 56
Solve the following equations:
4 \left( 3 x + 5\right) + 3 \left( 2 x + 6\right) = 74
2 \left( 2 x - 5\right) + 3 \left( 4 x + 6\right) = 56
2 \left( 4 x + 5\right) + 3 \left( 3 x - 6\right) = - 42
3 \left( 4 x + 6\right) - 2 \left( 3 x + 5\right) = 26
5 \left( 4 x - 6\right) - 3 \left( 2 x + 5\right) = - 73
8 \left( 4 x + 5\right) - 3 \left( 2 x - 6\right) = - 46
- 3 \left( 2 x + 5\right) + 5 \left( 4 x + 6\right) = 57
- 3 \left( 2 x + 5\right) + 5 \left( 3 x + 6\right) = 42
- 3 \left( 2 x + 6\right) + 5 \left( 4 x - 5\right) = - 15
- 3 \left( 2 x - 4\right) + 5 \left( 3 x + 5\right) = 55
- 3 \left( 2 x - 6\right) + 5 \left( 4 x - 5\right) = 21
- 3 \left( 2 x + 4\right) + 5 \left( 3 x + 5\right) = 40
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.