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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.
- Equation Form Comparison: When does an equation have infinitely many solutions? Infinitely many solutions occur when the two sides of the equation are identical in form, meaning that the coefficients of the variable terms and the constant terms are the same on both sides of the equation.
- Identifying Coefficients: We need to compare the coefficients of the variable terms and the constant terms on both sides of the equation.To have infinitely many solutions, the coefficients of and the constants must be the same on both sides.
- Matching Coefficients: Let's find the missing coefficient for that would make the left side of the equation identical to the right side.To match the coefficient of on the right side, which is , the missing coefficient on the left side must also be .So, the equation becomes .
- Checking Constants: Now, let's check if the constants are the same on both sides.The constant on the left side is , and the constant on the right side is also .Since they are the same, the equation will have infinitely many solutions with the missing coefficient being .
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