Question

1>) Find the missing number so that the equation has infinitely many solutions. 4(2x - 5) + x - 20 = -2(-5x + 20) Submit

Answer 1

Let a be the missing number. For the equation to have infinitely many solutions, both expressions on the left and on the right should be identical. Simplify both sides and then find which number a would make both expressions the same.

The left hand side expression is equal to:

`\begin{gathered} 4(2x-5)+ax-20=8x-20+ax-20 \\ =(8+a)x-40 \end{gathered}`

The right hand side expression is equal to:

`-2(-5x+20)=10x-40`

For those two expressions to be the same, the coefficient of x should be 10. Then:

`\begin{gathered} 8+a=10 \\ \Rightarrow a=2 \end{gathered}`

Therefore, the number that makes the equation to have infinitely many solutions is 2.