Solving linear equations and inequalitiesIB MYP Maths Standard: Subtopic test

1. 1
   Dev is solving equations for homework. His first equation is $5x-7=2x+11$.

   (a)

   Solve Dev's first equation.

   [1 mark]

   • A$x=\frac{4}{3}$
   • B$x=-6$
   • C$x=6$
   • D$x=\frac{18}{7}$

   (b)

   Which of these equations has the same solution as Dev's first equation?

   [1 mark]

   • A$x+3=9$
   • B$2x=18$
   • C$3(x-2)=24$
   • D$x-6=6$

   (c)

   Dev's second equation is $3(2x-1)=x+17$. Solve it.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Amira is solving the inequality $4x+3<2x+13$.

   (a)

   Solve the inequality.

   [1 mark]

   • A$x>5$
   • B$x<-5$
   • C$x<\frac{5}{3}$
   • D$x<5$

   (b)

   Which description shows the solution set $x<5$ on a number line?

   [1 mark]

   • AA filled circle at 5 with an arrow pointing left
   • BAn open circle at 5 with an arrow pointing left
   • CAn open circle at 5 with an arrow pointing right
   • DA filled circle at 5 with an arrow pointing right

   (c)

   Solve $7-3x\ge1$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Leila is solving equations that contain fractions.

   (a)

   Solve $\frac{3x+1}{4}=\frac{x+5}{2}$.

   [3 marks]

   (b)

   Solve $\frac{x}{2}+\frac{x-3}{4}=3$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Two number machines change an input $n$. Machine P multiplies $n$ by 3 and then subtracts 4. Machine Q adds 2 to $n$ and then multiplies the result by 2.

   (a)

   (i) Form and solve an equation to find the input that gives the same output from both machines.
   (ii) State this common output.
   (iii) Find all the inputs for which Machine P gives a larger output than Machine Q.

   [6 marks]

   (b)

   (i) The inputs to Machine Q are whole numbers from 0 to 12. Find the inputs for which Q gives an output less than 20, and describe how the solution of $2(n+2)<20$ is shown on a number line.
   (ii) Machine S subtracts $4n$ from 10. Find the inputs for which the output of S is at least 22.

   [6 marks]

   Total for question 4: 12 marks

End of questions