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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.
- Identical Form: 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.
- Determine Missing Coefficient: We need to determine the missing coefficient in front of on the left side of the equation so that it matches the coefficient on the right side.The equation is ____x + 10 = -2x + 10.To have infinitely many solutions, the coefficients of must be the same on both sides.
- Make Coefficients Same: To make the coefficients the same, the missing number in front of on the left side of the equation should be . So, the equation becomes .
- Check Constants: Now, we check if the constants are the same on both sides of the equation.The constants are both , so they are already the same.
- Infinitely Many Solutions: Since both the coefficients of and the constants are the same on both sides of the equation, the equation will have infinitely many solutions.
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