4.01 Review: One-step equations
Determine whether or not the given value of x is a solution to the following equations:
8 x = 51 where x = 6
2 x = 2 \times 4 where x = 4
\dfrac{x}{2} = 8 where x = 19
\dfrac{x}{3} = 8 where x = 24
For each of the following one-step equations, describe the step required to solve it:
x - 5 = 4
x - 4.5 = 6.8
9 x = 7 + 8 x
\dfrac{x}{4.1} = 7.6
4.1 x = 94.3
Solve:
x - 8 = - 20
x + 6 = 15
x + 12 = 9
21 = x + 13
x + 4 = 9
t - 15 = 0
x - 7 = 7
x - 4 = 10
7 = x - 1
6 = - 16 + n
n + 27 = 11
x - 21 = - 25
x - 3 = - 5
Solve:
x +2.4 = 7.2
x - 4.75= -10.25
x - 1.39 = 8.67
x - \dfrac{2}{5} = \dfrac{2}{5}
x + \dfrac{1}{5} = \dfrac{3}{5}
x - \dfrac{5}{8} = \dfrac{1}{8}
x - \dfrac{3}{4} = \dfrac{1}{8}
t - \dfrac{5}{8} = \dfrac{5}{7}
Solve:
5 x = 45
3 x = 18
10 t = 60
9 t = 3
7 t = 56
4 \times n = 20
88 = 11 \times n
12 = 3 x
\dfrac{x}{8} = 6
6 = \dfrac{x}{8}
\dfrac{t}{10} = 9
\dfrac{t}{6} = 10
\dfrac{x}{9} = 3
\dfrac{1}{8} x = 6
4 x = - 28
- 5 x = 30
- 7 x = 0
- 7 x = - 28
- x = 3
2 = - x
- 10 x = - 50
Solve:
- \dfrac{1}{8} x = 6
- 5 = \dfrac{x}{5}
- 6 = \dfrac{y}{- 7}
\dfrac{1}{8} x = - 8
- \dfrac{1}{8} x = - 8
88 = 11 n
4 n = 27.2
5.9n = 177
36.5 = 7.3 n
\dfrac{4}{9} n = 10
\dfrac{y}{- 5} = - 5
Find the number for each scenario:
When 10 is added to a number, the result is 12.
When a number is multiplied by 10, the result is 60.
Emilia and Dara are buying a \$350 kayak together. Emilia contributed \$m, and Dara contributed \$210.
Write an equation that represents the relationship between the amounts each contributed.
How much money did Emilia contribute to the kayak?
Kate and Isabelle do some fundraising for their sporting team. Together they raised \$600. If Kate raised \$272 more than Isabelle, and Isabelle raised \$p:
Write an equation in terms of p that represents the relationship between the different amounts and solve for p.
Finally, calculate how much Kate raised.