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Let's solve the problem step-by-step:
Step 1: Begin with the original equation:
.
Step 2: Simplify the left-hand side by combining like terms:
.
Step 3: Apply the distributive property to the right-hand side:
.
Step 4: Now the equation reads:
.
Step 5: Attempt to isolate the variable by subtracting from both sides:
.
This simplifies to:
.
Step 6: Subtract from both sides to further simplify the equation:
.
This is a contradiction, indicating that no solution exists for the equation since a statement like this is never true.
Therefore, the solution to the problem is No solution.
No solution
Solve for x:
\( 2(4-x)=8 \)
This means the equation has no solution! When variables completely cancel out and you're left with a false statement, the original equation is impossible to solve.
x = 0 is a valid solution where the variable equals zero. But 5 = 0 is a contradiction - it's saying 5 literally equals 0, which is impossible!
Not necessarily! Some equations genuinely have no solution. Double-check your algebra steps, but if you consistently get a contradiction, 'no solution' is the correct answer.
This happens when both sides of the equation have the same variable terms but different constant terms. Like - the variable parts are identical but constants differ.
You can write it as: No solution, ∅ (empty set symbol), or No real solutions exist. All are correct ways to express this.
Yes! Try substituting any number for the variable in the original equation. You'll find that no value makes both sides equal, confirming no solution exists.
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