Question

consider the equation 7a + 6 = ____ + 6. which value or expression can you write in the blank so the equation has no solution? 0, 6, 5a, 7a

Explanation:

Step1: Recall no - solution equation form

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 \(7a + 6=\underline{\quad}+ 0\), let the blank be \(mx + n\) (here \(n = 0\) for all options, so we focus on the coefficient of \(a\) and the constant term). The left - hand side (LHS) is \(7a+6\), the right - hand side (RHS) is \(\text{(blank)}+0\).

Step2: Analyze each option

• Option 0: The equation becomes \(7a + 6=0 + 0\), i.e., \(7a+6 = 0\). This is a linear equation with a solution (\(a=-\frac{6}{7}\)).
• Option 6: The equation becomes \(7a + 6=6+0\), i.e., \(7a+6 = 6\). Subtract 6 from both sides: \(7a=0\), so \(a = 0\) (has a solution).
• Option \(5a\): The equation becomes \(7a + 6=5a+0\). Subtract \(5a\) from both sides: \(2a+6 = 0\), then \(2a=-6\), \(a=-3\) (has a solution).
• Option \(7a\): The equation becomes \(7a + 6=7a+0\). Subtract \(7a\) from both sides: \(6 = 0\), which is a false statement. So the equation has no solution.

Answer:

\(7a\) (the option with \(7a\))