Question

Solving Linear Equations: Mastery Test

Answer 1

1. Solve for x: 2x + 5 = 11

First, we need to isolate x by getting rid of the constant term on the left side.

2x + 5 = 11
2x = 11 - 5
2x = 6

Next, divide both sides by 2 to solve for x:

x = 6/2
x = 3

Therefore, the solution to the equation 2x + 5 = 11 is x = 3.

2. Solve for y: 3y - 7 = 14

First, add 7 to both sides to eliminate the constant term on the left side:

3y - 7 + 7 = 14 + 7
3y = 21

Next, divide both sides by 3 to solve for y:

y = 21/3
y = 7

Therefore, the solution to the equation 3y - 7 = 14 is y = 7.

3. Solve for x: 4(x - 2) = 12

First, distribute the 4 on the left side of the equation:

4x - 8 = 12

Next, add 8 to both sides to eliminate the constant term on the left side:

4x - 8 + 8 = 12 + 8
4x = 20

Lastly, divide both sides by 4 to solve for x:

x = 20/4
x = 5

Therefore, the solution to the equation 4(x - 2) = 12 is x = 5.

4. Solve for y: 2y + 3 = 5y - 4

First, simplify the equation by moving all terms with y to one side of the equation:

2y - 5y = -4 - 3
-3y = -7

Finally, divide both sides by -3 to solve for y:

y = -7 / -3
y = 7/3

Therefore, the solution to the equation 2y + 3 = 5y - 4 is y = 7/3.

5. Solve for x: 3x + 4 = 7x - 2

First, simplify the equation by moving all terms with x to one side of the equation:

3x - 7x = -2 - 4
-4x = -6

Next, divide both sides by -4 to solve for x:

x = -6 / -4
x = 3/2

Therefore, the solution to the equation 3x + 4 = 7x - 2 is x = 3/2.