Linear inequalities — Heart of Algebra

Questions in this quiz (9)

1. Solve: $$5x-2 \geq 13$$

   • $$(-\infty, 3)$$
   • $$(-3, \infty)$$
   • $$[-3, \infty)$$
   • $$[3, \infty)$$

2. Solve: $$\frac{x}{4}+1 \leq 5$$

   • $$x$$ > $$16$$
   • $$x \geq 16$$
   • $$x \leq 16$$
   • $$x$$ < $$16$$

3. Solve: $$2(x-3)$$ > $$10$$

   • $$[8, \infty)$$
   • $$(8, \infty)$$
   • $$(-\infty, 8)$$
   • $$(-\infty, 8]$$

4. Solve: $$\frac{3x-9}{6} \geq 2$$

   • $$x \geq 7$$
   • $$x$$ < $$21$$
   • $$x$$ > $$7$$
   • $$x \leq 12$$

5. Solve: $$-2x+1 \leq -5$$

   • $$[3, \infty)$$
   • $$(3, \infty)$$
   • $$(-\infty, 3)$$
   • $$(-\infty, 3]$$

6. Solve: $$3(2x+1)$$ > $$12$$

   • $$x$$ > $$3$$
   • $$x$$ > $$\frac{3}{2}$$
   • $$x$$ < $$\frac{2}{3}$$
   • $$x$$ > $$2$$

7. Jasmine bought two bags of marbles. In the first bag, $$40\%$$ of the marbles are blue, and in the second bag, $$55\%$$ of the marbles are blue. Together, the bags contain at least $$500$$ blue marbles. Which inequality represents this situation, where $$x$$ is the number of marbles in the first bag and $$y$$ is the number of marbles in the second bag?

   • $$0.4x+0.55y\geq500$$
   • $$0.5x+0.4y\geq500$$
   • $$4x+5.5y\geq500$$
   • $$0.4x+0.55y\leq500$$

8. Tom scored $$92$$, $$81$$, and $$87$$ on his first three science exams. Which inequality gives the score, $$S$$, Tom must earn on his fourth exam so that his average score on all four exams will be at least $$90$$?

   • $$90-(92+81+87)\le4S$$
   • $$4S+92+81+87\ge360$$
   • $$\frac{S+92+81+87}{4}\ge90$$
   • $$\frac{92+81+87}{4}\ge90-4S$$

9. What is the smallest possible value for $$x$$ in the inequality:$$-3x+4\le-8$$?

   • $$-4$$
   • $$-\frac{4}{3}$$
   • $$0$$
   • $$4$$