Question

2 Sarah attempted to solve the equation -x + 5(x + 6) = 4x + 30 as shown, and concluded that there are no solutions. Solve the equation, explain Sarah’s error, and find the correct number of solutions.

Answer 1

There are infinite answers

Explanation:

Step 1: Simplify both sides of the equation.

−x+5(x+6)=4x+30

−x+(5)(x)+(5)(6)=4x+30(Distribute)

−x+5x+30=4x+30

(−x+5x)+(30)=4x+30(Combine Like Terms)

4x+30=4x+30

4x+30=4x+30

Step 2: Subtract 4x from both sides.

4x+30−4x=4x+30−4x

30=30

Step 3: Subtract 30 from both sides.

30−30=30−30

0=0

Sarah's error is she multiplied -x times 5x but not 6

There are infinite amount of answers