4.03 Multistep equations
Solve:
9 \left( x + 2 \right) = 27
2 \left( p + 9 \right) = 28
6 \left( x + 5 \right) = 54
13 \left( s - 7 \right) = 143
4 \left(k - 4\right) = 48
Solve:
3 \left( 4 s + 1\right) = - 21
3 \left( 2 x + 1\right) = 15
2 \left( 3 t - 7\right) = 16
- 5 \left( 3 x + 8\right) = - 10
2 \left( - 3 g + 7\right) = - 16
- 2 \left( 3 x - 5\right) = 28
- 3 \left( - 2 h - 5\right) = 33
- 3 \left( - 2 x + 7\right) = -45
4 \left( 5 x - 1\right) = - 24
- 4 \left( 5 x + 6\right) = - 104
2 \left( 7 + 2x \right) = 38
- 3 \left( 4 - x \right) = - 12
5 \left( 2 x - 6 \right) = 100
6 \left( 3 x + 15 \right) = -72
9 \left( 8 - x \right) = 45
10 \left( 7 - 3x \right) = 20
20 = 2 \left( 3x + 11 \right)
16 = 4 \left(2x + 9\right)
18 = 3 \left( 2x + 14 \right)
-5 = 5 \left(3x + 1\right)
26 = 13 \left( 8 - 4x \right)
32 = 8 \left(16 - 5x\right)
Ryan attempted to solve the equation 9 \left( 4x - 6 \right) = 18. His work 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:
3 \left(w + 8\right) + 5 = 44
9 \left(x - 7\right) + 8 = 26
- 5 \left(g + 4\right) + 9 = - 41
- 7 \left(x + 5\right) + 4 = - 17
6 \left(q + 1\right) - 5 = - 23
4 \left(x + 6\right) - 8 = 48
-8 \left(x + 4\right) - 3 = - 59
- 2 \left(x - 2\right) - 7 = - 29
2 \left(x - 9\right) - 4 = 16
5 \left(x - 3\right) - 7 = - 52
Solve:
- \dfrac{y}{3} + 10 = 17
- \dfrac{u}{4} + 15 = 8
\dfrac{5 x}{8} - 9 = - 4
\dfrac{8 c}{3} + 5 = - 11
\dfrac{5 x}{3} + 11 = 21
\dfrac{- 3 c}{4} + 5 = 14
- \dfrac{3 x}{4} + 5 = - 7
\dfrac{3 x}{4} - 5 = - 11
\dfrac{4 x}{7} - 6 = - 14
- \dfrac{5 x}{6} - 6 = 14
Solve:
\dfrac{x - 9}{5} + 4 = 7
\dfrac{x - 3}{5} - 8 = - 7
\dfrac{x + 2}{3} - 25 = - 22
\dfrac{x + 16}{3} + 5 = 3
\dfrac{2 x - 12}{3} = 0
\dfrac{3 x + 6}{2} = 15
\dfrac{8 x + 4}{5} = - 4
\dfrac{- 3 t - 6}{7} = - 3
\dfrac{- 13 - 4 r}{3} = - 15
\dfrac{- 9 + 5 x}{2} = - 22
Solve:
Solve:
Solve:
\dfrac{x}{6} = \dfrac{5}{3}
\dfrac{7}{9} = \dfrac{4}{x}
\dfrac{x}{6} = 2\dfrac{2}{3}
\dfrac{7.8}{7.5} = \dfrac{x}{5}
\dfrac{n}{6} + \dfrac{n}{5} = 11
\dfrac{x}{5} - \dfrac{x}{2} = 3
\dfrac{- x}{5} + \dfrac{x}{3} = 4
\dfrac{- x}{5} - \dfrac{x}{7} = - 24
\dfrac{9 x}{3} + \dfrac{9 x}{2} = - 5
\dfrac{3 x}{5} - \dfrac{4 x}{6} = - 5
\dfrac{5 x}{3} - 3 = \dfrac{3 x}{8}
\dfrac{3 x}{2} + 5 = \dfrac{2 x}{3}
\dfrac{2 x}{3} - 2 = \dfrac{5 x}{2} + 4
\dfrac{8 x}{3} + 4 = \dfrac{7 x}{4} - 6
\dfrac{8 x - 2}{3} = \dfrac{6 x - 3}{4}
\dfrac{6 x + 3}{3} = \dfrac{7 x - 2}{5}
x + \dfrac{5 x-1}{4} = 1
\dfrac{2 x - 3}{6} - \dfrac{3 x - 2}{5} = - 5
x + \dfrac{3 x + 4}{2} = 3
\dfrac{5 x - 1}{3} - \dfrac{2 x - 4}{5} = - 1
The formula to convert temperature from Celsius to Fahrenheit is F = 32 + \dfrac{9 C}{5}.
If C = 35, find the value of F.
If F = 212, find the value of C.
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}.
Solve the equation \dfrac{3000 x + 22\,500\,000}{x} = 6000 to find the number of cranes that must be sold for the cost of development and production to be \$6000.