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Find the missing number so that the equation has infinitely many solutions.
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Q. Find the missing number so that the equation has infinitely many solutions.
- Identify Condition: Identify the condition for infinitely many solutions.For an equation to have infinitely many solutions, the expressions on both sides of the equation must be identical. This means that the coefficients of the variable and the constant terms must be the same on both sides of the equation.
- Set Up Equation: Set up the equation with the missing number.The given equation is ____x + 5 = 5x + 5. To have infinitely many solutions, the coefficient of on the left side must be the same as the coefficient of on the right side, which is .
- Determine Missing Number: Determine the missing number.Since the coefficients of must be equal for the equation to have infinitely many solutions, the missing number is .
- Verify Solution: Verify the solution.If we replace the missing number with , we get . Both sides of the equation are identical, confirming that the equation will indeed have infinitely many solutions.
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