Quiz 2: PSAT 8/9 Linear Equations — Heart of Algebra: Linear Equations

Questions in this quiz (10)

1. A rope that is $$150$$ centimeters long is cut into three pieces. One piece is $$60$$ cm long. The other two pieces are equal in length. What is the length, in cm, of each of the other two pieces?

   • $$30$$
   • $$40$$
   • $$45$$
   • $$50$$

2. Maria has $$n$$ books. Luis has $$5$$ more than three times the number of books that Maria has. In terms of $$n$$, how many books does Luis have?

   • $$3n-5$$
   • $$3n+5$$
   • $$5n+3$$
   • $$n+15$$

3. If $$3x+4=16$$, what is the value of $$5x-2$$?

   • $$14$$
   • $$16$$
   • $$18$$
   • $$20$$

4. If $$6-3(2-x)=12-2(2-x)$$, what is the value of $$2-x$$?

   • $$-8$$
   • $$-6$$
   • $$6$$
   • $$8$$

5. If $$4(x+3)=3(x+3)+10$$, what is the value of $$x+3$$?

   • $$7$$
   • $$8$$
   • $$9$$
   • $$10$$

6. If $$8(5-2x)+4=6(5-2x)+20$$, what is the value of $$5-2x$$?

   • $$-8$$
   • $$-4$$
   • $$4$$
   • $$8$$

7. The perimeter of an isosceles triangle is $$70$$ inches. Each of the two equal sides is $$25$$ inches long. What is the length, in inches, of the third side?

   • $$15$$
   • $$20$$
   • $$25$$
   • $$45$$

8. Each side of a $$24$$-sided polygon has one of three lengths. The number of sides with length $$6$$ cm is $$4$$ times the number of sides $$n$$ with length $$2$$ cm. There are $$8$$ sides with length $$5$$ cm. Which equation must be true for the value of $$n$$?

   • $$4n+8=24$$
   • $$5n+8=24$$
   • $$6n+8=24$$
   • $$4n+5n+8=24$$

9. If $$2(x-5)+3(x-5)=10$$, what is the value of $$x-5$$?

   • $$2$$
   • $$5$$
   • $$7$$
   • $$12$$

10. Consider the equation:$$-49x=-98x$$.How many solutions does the equation have?

    • $$\text{Zero}$$
    • $$\text{Exactly one}$$
    • $$\text{Exactly two}$$
    • $$\text{Infinitely many}$$