Linear Equations (Advanced)

Linear Equations: core idea

• 1. A $240$-mile trip is driven partly at $50$ mph and partly at $70$ mph. If it takes $4$ hours, how many miles were driven at $50$ mph?

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• 2. The line through $(a,4)$ and $(6,10)$ has slope $\frac32$. Find $a$.

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• 3. Solve $|3x-8|=13$. Give the negative solution.

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• 4. A fundraiser has adult tickets at $12$ dollars and student tickets at $7$ dollars. It sells $83$ tickets for $771$ dollars. How many adult tickets were sold?

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• 5. For what value of $c$ does $y=\frac{c}{x-2}$ pass through $(5,4)$?

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• 6. If $\frac{2x+1}{x-3}=5$, find $x$.

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• 7. The solutions to $ax+9=3(x+5)$ are all real numbers. Find $a$.

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• 8. A tank is $\frac25$ full. After $18$ gallons are added, it is $\frac34$ full. What is its capacity?

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• 9. The mean of $x$, $x+4$, and $3x-2$ is $18$. Find $x$.

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