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Quiz 7
1.) Find three consecutive numbers whose sum is $36$.
Solution: Let $x$ be the smallest of the three numbers, then the other two are $x+1$ and $x+2$. To say that their sum is $36$ means we must solve the equation $$x+(x+1)+(x+2)=36.$$ Simplify the left-hand side to get $$3x+3=36.$$ Now subtract $3$ to get $$3x = 33.$$ Now divide by $3$ to get $$x=11.$$ Therefore the three numbers are $11$, $12$, and $13$.

2.) Solve and graph $3x+1 < 4$.
Solution: To solve it, first subtract $1$ from both sides to get $$3x < 3.$$ Now divide by $3$ on both sides to get $$x < 1.$$

3.) Solve and graph $-2x+1>5$.
Solution: Subtract $1$ to get $$-2x > 4.$$ Divide by $-2$ and flip the inequality symbol to get $$x < -2.$$

4.) Solve and graph $\dfrac{1}{2}x + \dfrac{1}{4} \geq \dfrac{1}{4}$.
Solution: Subtract $\dfrac{1}{4}$ to get $$\dfrac{1}{2}x \geq 0.$$ Multiply by $2$ to get $$x \geq 0.$$

5.) Solve and graph $-x+1 \leq x-1$.
Solution: Add $-x$ to both sides to get $$-2x + 1 \leq -1.$$ Subtract $1$ from both sides to get $$-2x \leq -2.$$ Divide by $-2$ and flip the inequality to get $$x \geq 1.$$