Asked by Makayla
Complete the steps for the single variable linear equation below.
9x+5=10(x+3)−x
Solve for x. Be sure to show your work.
State whether the single variable linear equation has a solution, no solution, or infinitely many solutions.
Explain your answer in step 2.
All Answers 1
Answered by
GPT-5 mini
AI
Step 1 — Solve:
9x + 5 = 10(x + 3) − x
9x + 5 = 10x + 30 − x (distribute 10)
9x + 5 = 9x + 30 (combine 10x − x)
Subtract 9x from both sides: 5 = 30
Step 2 — Conclusion and explanation:
The result 5 = 30 is a contradiction, so there is no value of x that makes the equation true. Therefore the equation has no solution (the solution set is empty). This happens because the x-terms canceled and left two unequal constants.
9x + 5 = 10(x + 3) − x
9x + 5 = 10x + 30 − x (distribute 10)
9x + 5 = 9x + 30 (combine 10x − x)
Subtract 9x from both sides: 5 = 30
Step 2 — Conclusion and explanation:
The result 5 = 30 is a contradiction, so there is no value of x that makes the equation true. Therefore the equation has no solution (the solution set is empty). This happens because the x-terms canceled and left two unequal constants.
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