5.01 Solving equations
For each of the following equations, describe what must be done to both sides in order to solve the equation:
x - 4 = 6
For each of the following equations:
Describe how to make the variable the subject of the equation.
Solve the equation.
5 p = - 50
- \dfrac{n}{9} = 4
Solve the following equations:
8 k = - 48
- 7 m = 63
5 m = 11
p + 36 = 62
24 + p = - 2
\dfrac{t}{5} = 1.6
v + 41 = 4
\dfrac{q}{5} = - 4
Use substitution to determine whether the given value of x is the solution to each equation:
x - 10 = - 1 where x = 9
x - 4 = - 5 where x = 0
x + 1 = 7 where x = 6
x - 3 = - 3 where x = 3
8 x = 51 where x = 6
2 x = 8 where x = 4
3 x + 1 = 7 where x = 2
6 x - 13 = 12 where x = 4
5 x + 12 = 31 where x = 4
4 x - 2 = 18 where x = 5
\dfrac{x}{2} = 8 where x = 19
\dfrac{x}{3} = 8 where x = 24
Solve the following equations:
3 x + 11 = 5
12 q + 8 = 26
4 s - 9 = 39
- 6 s + 5 = 47
6 t + 2 = - 22
Solve the following equations:
\dfrac{5 x}{6} = 11
\dfrac{x + 15}{2} = 5
\dfrac{4n}{9} = 10
\dfrac{x}{7} + 13 = 21
\dfrac{m - 6}{4} = 4.25
\dfrac{n + 36}{2} = 11
\dfrac{x}{7} + 19 = 16
\dfrac{- 44}{p} = 11
\dfrac{4}{q} = 28
\dfrac{30}{q} = - 5
\dfrac{r - 6}{4} = - 6
\dfrac{w}{2} + 14 = 6
Solve the following equations:
2 \left(q + 11\right) = 20
3 \left(q + 3\right) = - 18
2 \left(p + 6\right) = - 8
7 \left(11 - n\right) = 210
- 4 \left(r + 5\right) = - 44
2 \left(u + 2\right) = - 8
2 \left(u + 5\right) = 18
4 \left(u - 4\right) = - 36