Solutions of an Equation

• one solution

• no solution

• infinite solutions

Level 4: For what values of a and b will the equation have ONE SOLUTION?

5(2x+3) - 6 = ax + b

• a = 10, b = 15

• a = 10, b = 9

• a = 7, b = 11

Level 4: For what values of a and b will the equation have INFINITELY MANY SOLUTIONS?

5(2x+3) - 6 = ax + b

• a = 10, b = 15

• a = 10, b = 9

• a = 7, b = 11

Level 3 Fill in the blank (question mark) to create an equation with INFINITELY MANY SOLUTIONS?

-5x + 4 = -5x - ?

• -5

• 5

• 4

• -4

Which of the following equations has only one solution?

• x + 4 = x + 3

• -2x + 4 = -2x - 4

• 3x = 3x

• 4x - 2 = 2x - 4

When x = 5 in the equation
x + 7 = 15
(5) + 7 = 15
12 = 15
TRUE OR FALSE?

• TRUE

• FALSE

What is the solution to the equations?

• one solution

• no solution

• infinite solutions

• none of these

Answer explanation

The equations have the same slope and y-intercept, indicating they represent the same line. Therefore, there are infinite solutions where any point on the line satisfies both equations.

• one solution

• no solution

• infinite solutions

Answer explanation

The equation 9-x=-x+9 simplifies to 9=9, which is always true. This means any value of x satisfies the equation, resulting in infinite solutions.

• one solution

• no solution

• infinite solutions

Answer explanation

To solve the equation 4-2x=2x-4, combine like terms to get 4+4=2x+2x, which simplifies to 8=4x. Dividing both sides by 4 gives x=2. Thus, there is one solution: x=2.

• one solution 

• no solution

• infinite solutions

Answer explanation

The equation 8x + 1 = 8x + 1 is true for all values of x, as both sides are identical. This means there are infinite solutions, as any value of x satisfies the equation.