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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
$$x \geq 1.$$
