Question

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Explanation:

Step1: Recall no - solution equation condition

For a linear equation of the form \(ax + b=cx + d\), if \(a = c\) and \(b
eq d\), the equation has no solution. The given equation is \(7x+6=\underline{\quad}+9\). Let the blank be \(mx + n\) (in the case of linear terms) or a constant. We can rewrite the equation as \(7x+6=mx + n + 9\), or \(7x+6=mx+(n + 9)\).

Step2: Analyze each option

• Option 0: The equation becomes \(7x + 6=0 + 9\), i.e., \(7x+6 = 9\). Subtract 6 from both sides: \(7x=9 - 6=3\), then \(x=\frac{3}{7}\). This equation has a solution.
• Option 6: The equation becomes \(7x + 6=6 + 9\), i.e., \(7x+6 = 15\). Subtract 6 from both sides: \(7x=15 - 6 = 9\), then \(x=\frac{9}{7}\). This equation has a solution.
• Option \(5x\): The equation becomes \(7x+6 = 5x+9\). Subtract \(5x\) from both sides: \(7x-5x+6=9\), \(2x+6 = 9\). Subtract 6 from both sides: \(2x=9 - 6 = 3\), then \(x=\frac{3}{2}\). This equation has a solution.
• Option \(7x\): The equation becomes \(7x+6=7x + 9\). Subtract \(7x\) from both sides: \(7x-7x+6=9\), which simplifies to \(6 = 9\). Since \(6

eq9\), this equation has no solution.

Answer:

To make the equation \(7x + 6=\underline{\quad}+9\) have no solution, we put \(7x\) in the blank. So the value or expression is \(7x\).