3.02 Review: One-step equations
Write the new equation produced for each of the following scenarios:
Add 1 to both sides of x = 9
Subtract 7 from both sides of x = 14
Multiply 5 to both sides of x = 10
Divide 11 to both sides of x = 99
Add 4 to both sides of x = - 6
Subtract 20 from both sides of x = 2
Multiply 8 to both sides of x = - 3
Divide 5 to both sides of x = - 25
Multiply 11 to both sides of 5 x = 6
Multiply 12 to both sides of 3 x = - 8
Divide 3 to both sides of 9 x = 27
Divide 9 to both sides of 45 x = - 54
Multiply \dfrac{7}{8} to both sides of 5 m = 3
Multiply \dfrac{1}{3} to both sides of - 4 x = 5
Determine whether 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
x - 10 = - 1 where x = 9
x - 4 = - 5 where x = 0
x + 1 = 7 where x = 6
x - 3 = - 3 where x = 3
For each of the following one-step equations, describe the step required to solve it:
x + 3 = 4
8 + x = -11
x - 5 = 4
x - 4.5 = 6.8
\dfrac{x}{2} = 18
65 x = 520
\dfrac{x}{4.1} = 7.6
4.1 x = 94.3
Solve:
x + 6 = 15
x + 4 = 9
t - 15 = 0
x - 7 = 7
21 = x + 13
x - 4 = 10
7 = x - 1
x - 8 = - 20
x + 12 = 9
6 = - 16 + n
n + 27 = 11
x - 21 = - 25
x - 3 = - 5
9.12 + x = 15.44
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
12 = 3 x
3 x = 18
10 t = 60
5.9n = 177
4n = 27.2
4n = 20
88 = 11n
36.5 = 7.3n
9 t = 3
7 t = 56
-0.16x = 1.92
\dfrac{t}{10} = 9
\dfrac{t}{6} = 10
\dfrac{x}{9} = 3
\dfrac{x}{8} = 6
6 = \dfrac{x}{8}
\dfrac{1}{8} x = 6
\dfrac{2}{3} x = 6
-\dfrac{21}{2} = \dfrac{7}{10}x
Use an equation to find the unknown number for each of the following:
When 10 is added to a number, the result is 12.
When a number is multiplied by 10, the result is 60.
When 20 is subtracted to a number, the result is 5.
The sum of a number and 39 is 83.
The product of 3 and a number is 18.
17 less than a number is 25.
The quotient of a number and 8 is -12.
John and Uther do some fundraising for their sporting team. Together they raised \$403. If John raised \$ m, and Uther raised \$71:
Write an equation that represents the relationship between the amounts each contributed.
Find the value of m.
Justin divides a deck of cards into 7 even groups. There are 12 cards in each group. Let c be the total number of cards in the deck.
Write down the equation that represents the relationship between the total number of cards in the deck and the number of cards in each group.
Now, solve the equation.
Kate and Isabelle do some fundraising for a charity. 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 then solve for p.
How much did Kate raise?
Athena wants to go karting. It costs 50 cents per lap of the course. Athena has \$12 to spend.
Write an equation for the number of laps, n, that Athena can afford.
Solve for the number of laps Athena can afford.