Question

Select the phrase that best completes the sentence.

Consider the equation
.

The equation has
no solution
.

Answer 1

I don't see the equation — can you paste it? I need the actual equation to choose the correct phrase.

Meanwhile, here are quick rules you can use to decide when "no solution" is correct:

- After simplifying the equation, if you get a contradiction like 0 = nonzero (for example 2x + 3 = 2x + 5 simplifies to 0 = 2), then the equation has no solution.
- For linear equations in one variable: if coefficients of the variable cancel and the remaining constants are unequal → no solution.
- For quadratics (real solutions): if the discriminant b^2 − 4ac < 0, the quadratic has no real solutions (but two complex ones).
- For absolute-value equations: if you end up requiring an expression that cannot be true (for example |something| = −3) → no solution.
- For systems of linear equations: if the equations represent parallel lines (same slope, different intercept) → no solution (inconsistent system).

If you post the exact equation I’ll determine which phrase fits and show the steps.