Solve for x:
x + 4 = 9
7 = x - 1
- 5 x = 30
\dfrac{x}{8} = 6
- 5 = \dfrac{x}{5}
4 x = - 28
\dfrac{1}{7}x = 6
x - 1.39 = 8.67
State whether the following statements are true or false:
x = 9 is a solution for the equation x - 10 = - 1
x = 0 is a solution for the equation x - 4 = - 5
x = 6 is a solution for the equation x + 1 = 7
x = 3 is a solution for the equation x - 3 = - 3
Find the value of t if 10 t = 60.
Solve - 6 = -\dfrac{y}{7}.
The following equations contain a geometric figure which represents a non-zero real number.
If \triangle =- x, state whether the following are true or false:
\triangle =x
x=-(-\triangle)
x=\triangle
x=-\triangle
State whether the following statements are true or false:
x = 6 is a solution for the equation 2 \left(x - 3\right) = - 8.
x = 8 is a solution for the equation 7 \left(x - 6\right) = 14.
x = 8 is a solution for the equation 3 \left(x - 6\right) = 6.
x = 8 is a solution for the equation 9 = 7 \left(x - 7\right).
Solve the following equations:
8 m + 9 = 65
5 x - 8 = 2
7 x + 14 = 0
- x - 7 = 7
- 6 x + 4 x - 3 x = 0
- 6 + 2 k = 10
5 \left(y + 1\right) = 25
3 \left(5 - x\right) = 0
\dfrac{x}{2} + 8 = 10
\dfrac{x}{2} - 3 = 2
\dfrac{x + 9}{7} = 4
\dfrac{c - 4}{4} = 7
- \dfrac{1}{8} x = 6
\dfrac{x}{6} = \dfrac{5}{3}
\dfrac{x}{6} = 2\dfrac{2}{3}
\dfrac{7.8}{7.5} = \dfrac{x}{5}
If the equation 5 y + 8 = c has a solution of y = 5, find the value of c.
Solve the following equations:
5 x + 2 = 3 x + 22
8 x - 11 = 4 x
- 107 - 8 x = - 17 x + 19
- 64 - 9 x = - 24 - x
2 \left(x - 2\right) = x - 4
4 \left(x + 9\right) = x - 9
3 x = - 13 - 4 \left( 2 x + 5\right)
- 2 \left(x + 2\right) - 6 = - 20
Solve the following equations:
3 x + 2 \left( 3 x + 1\right) = 11
5 x - 2 \left( - 4 x - 5\right) = - 42
7 \left(x - 6\right) = 5 \left(x + 2\right)
2 \left( 2 x + 5\right) = 3 \left(x + 5\right)
5.3 \left( 3 x + 55\right) = 4.9 \left(x + 55\right)
3 \left(x + 6\right) + 3 \left(x + 24\right) = 12
5 \left(x + 4\right) + 3 \left( - x + 2\right) = - 6
4 \left(x + 10\right) - 2 \left(x + 8\right) = 0
5 \left( 2 x + 2\right) = - 3 \left( 4 x - 5\right) + 5 x
9 \left(x - 9\right) - \left(x + 54\right) = 63 - \left(x - 63\right)
Consider the equation 3 k + 4 = A k - 2. If k = 6, find the value of A.
Solve \dfrac{2}{1.1} = \dfrac{5}{x}.
State whether we can immediately use cross multiplication to solve the following equations:
\dfrac{5 - x}{6} = \dfrac{2 + x}{7}
\dfrac{2}{3} - x = \dfrac{5 + x}{5}
Solve the following equations:
\dfrac{ x - 1}{3} = \dfrac{ x}{4}
\dfrac{ x}{4} = \dfrac{2x+1}{5}
\dfrac{2 x - 1}{3} = \dfrac{ x - 2}{4}
\dfrac{8 x - 2}{3} = \dfrac{6 x - 3}{4}
Solve the following equations:
\dfrac{5 x}{6} + 4 = 21.5
Solve the following equations:
\dfrac{10 x - 26}{2} + 3 = 4 x
x + \dfrac{5 x-1}{4} = 1
\dfrac{n}{2} + \dfrac{n}{3} = 15
\dfrac{x}{5} - \dfrac{x}{2} = 3
\dfrac{9 x}{3} + \dfrac{9 x}{2} = - 5
\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
A construction company has spent \$22\,500\,000 to develop new cranes, and wants to limit the cost of development and production of a single 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.
Write an expression for the cost of one crane.
If the cost of one crane must equal \$6000, find x, the number of cranes that must be sold.