Solving Linear Equations: Variables on Both Sides

Which number can each term of the equation be multiplied by to eliminate the decimals before solving? 5.6j - 0.12 = 4 + 1.1j

100

Solve the equation. -3x + 1 + 10x = x + 4

x = 1/2

The International Business Club starts the school year with $250.50 in their account. They spend $35 each month on activities. The Future Agricultural Leaders Club starts with $300 and spends $45.25 each month. Which equation can be used to find m, the number of months it will take for both accounts to have the same amount of money?

250.5 - 35m = 300 - 45.25m

Which number can each term of the equation be multiplied by to eliminate the fractions the fractions before solving? -3/4m -1/2 = 2 + 1/4m

4

What is the solution to the linear equation? 4b + 6 = 2 - b + 4

b = 0

What is the solution to the linear equation? d - 10 - 2d + 7 = 8 + d - 10 - 3d

d = 1

What is the solution to the linear equation? 2/5 + p = 4/5 + 3/5p

p = 1

Which number can each term of the equation be multiplied by to eliminate the decimals before solving? -m + 0.02 + 2.1m = -1.45 _ 4.81m

100

Which number can each term of the equation be multiplied by to eliminate the fractions before solving? 6 - 3/4x + 1/3 = 1/2x + 5

12

What is the justification for the step taken from line 2 to line 3? 3x + 9 - 7x = x + 10 + x

the subtraction property of equality

Solve the equation. y + 3 = -y + 9

y = 3

What is the solution to the linear equation? 2.8y + 6 + 0.2y = 5y - 14

y = 10

Solve the equation. y + 6 = -3y + 26

y = 5

The levels of mercury in two different bodies of water are rising. In one body of water the initial measure of mercury is 0.05 parts per billion (ppb) and is rising at a rate of 0.1 ppb each year. In the second body of water the initial measure is 0.12 ppb and the rate of increase is 0.06 ppb each year. Which equation can be used to find y, the year in which both bodies of water have the same amount of mercury?

0.05 + 0.1y = 0.12 + 0.06y

Solve the equation. 8 - 2x = -8x + 14

x = 1

What is the solution to the linear equations? 2/3x - 1/2 = 1/3 + 5/6x

x = -5

Two runners are saving money to attend a marathon. The first runner has $112 in savings, received a $45 gift from a friend, and will save $25 each month. The second runner has $50 in savings and will save $60 each month. Which equation can be used to find m, the number of months it will take for both accounts to have the same amount of money?

112 + 25m + 45 = 50 + 60m

What is the solution to the linear equation? 6k + 10.5 = 3k + 12

k = 0.5