Solving Equations with Variables on Both Sides

What is the first step to solve this equation:

11 - 3x = 44

• Add 3 to both sides

• Subtract 11 from both sides

• Add 11 to both sides

• Divide 3 on both sides.

Translate into an equation:

3 times r less than 15 is 6.

• 3r - 15 = 6

• 15 - 3r = 6

• 3(r - 15) = 6

• 3(15-r) = 6

Solve for x:

5x - 14 = 8x + 4

• x = 6

• x = -6

• x = -18/13

• x = 10/3

Solve for n:

-(8n - 2) = 3 + 10(1 - 3n)

• n = 1/2

• n = -1/2

• n = 2

Solve for y:

3(y + 1) - 5 = 3y - 2

• infinitely many solutions

• no solution

• -2 = -2

• x = 0

Solve for f:

f - 4 = 6f + 26

• f = -5

• f = 5

• f = 6

• f = -6

Solve for x:

4(1-x) + 3x = -2(x+1)

• x = -6

• x = 6

• x = 3

Solve for x:

x + 2 = x + 4

• infinitely many solutions

• no solution

• x = 0

• 2 = 4

Find four consecutive integers with the sum -142.

• -38, -37, -36, -35

• -39, -38, -37, -36

• -40, -39, -38, -37

• -37, -36, -35, -34

Break-Even Problem!

Joe’s Canoes charges an initial fee of $20 plus $4 an hour. Callie’s Canoes charges a flat rate of $14 an hour. Find the number of hours for which the total amount that both places charge would be the same.

• 3 hours

• 4 hours

• 1 hour

• 2 hours