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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 Equation Pattern: Understand when an equation has infinitely many solutions. An equation has infinitely many solutions when both sides of the equation are identical. This means that the coefficients of the variable and the constant terms must be the same on both sides of the equation.
- Compare Coefficients of x: Compare the coefficients of x on both sides of the equation.For the equation ____x + 18 = 5x + 18 to have infinitely many solutions, the coefficient of x on the left side must be the same as the coefficient of x on the right side, which is .
- Set Coefficients Equal: Set the missing coefficient equal to the known coefficient.The missing coefficient of on the left side should be set to to satisfy the condition for infinitely many solutions.
- Verify Constant Terms: Verify that the constants are the same on both sides.The constants on both sides of the equation are already the same, which is . This confirms that setting the missing coefficient to will result in an equation with infinitely many solutions.
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